Beyond the random walk: A guide to stock market anomalies and low risk investingDocument Transcript
Beyond the Random Walk:
A Guide to Stock Market
Anomalies and Low-Risk
VIJAY SINGAL, PH.D., CFA
OXFORD UNIVERSITY PRESS
BEYOND THE RANDOM WALK
Financial Management Association
Survey and Synthesis Series
The Search for Value: Measuring the Company’s Cost of Capital
Michael C. Ehrhardt
Managing Pension Plans: A Comprehensive Guide to Improving
Dennis E. Logue and Jack S. Rader
Efficient Asset Management: A Practical Guide to Stock Portfolio
Optimization and Asset Allocation
Richard O. Michaud
Real Options: Managing Strategic Investment in an Uncertain World
Martha Amram and Nalin Kulatilaka
Beyond Greed and Fear: Understanding Behavioral Finance and the
Psychology of Investing
Dividend Policy: Its Impact on Form Value
Ronald C. Lease, Kose John, Avner Kalay,
Uri Loewenstein, and Oded H. Sarig
Value Based Management: The Corporate Response to Shareholder
John D. Martin and J. William Petty
Debt Management: A Practitioner’s Guide
John D. Finnerty and Douglas R. Emery
Real Estate Investment Trusts: Structure, Performance, and Investment
Su Han Chan, John Erickson, and Ko Wang
Trading and Exchanges: Market Microstructure for Practitioners
A Guide to Stock Market
Anomalies and Low-Risk
This book is dedicated to my wife, Manisha,
and my teenage sons, Ashish and Akshay,
who, apparently believing that the book is perfect,
refused to read beyond the title page.
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1 Market Efficiency and Anomalies 1
2 The January Effect and the New December Effect 23
3 The Weekend Effect 40
4 Short-Term Price Drift 56
5 Momentum in Industry Portfolios 78
6 Mispricing of Mutual Funds 104
7 Trading by Insiders 134
8 Changes to the S&P 500 Index 163
9 Merger Arbitrage 196
10 International Investing and the Home Bias 232
11 Bias in Currency Forward Rates 259
12 Understanding and Learning from Behavioral Finance 284
13 A Description of Other Possible Mispricings 298
APPENDIX A: Financial Instruments 318
APPENDIX B: Short Selling 323
APPENDIX C: Hedging Market Return 328
This book is about anomalies in financial markets. While most people
believe that markets are generally efficient, there is a consensus that
pockets of inefficiency exist within broad market efficiency. Both
academics and practitioners share this view. As a finance professor
remarks, “You find more and more academics willing to concede
that the market doesn’t look as efficient as they once thought.” For
instance, Gus Sauter, who runs Vanguard Group’s massive stock
indexing operations, valued at over $100 billion, says, “I don’t be-
lieve markets are perfectly efficient.”1
In an attempt to discover market inefficiencies, academics and
practitioners have expended tens of thousands of man-years re-
searching mispricings and anomalies. As the April 2001 issue of the
Journal of Finance notes, “[T]housands of papers have . . . investi-
gated the statistical behavior of stock returns and the extent to which
stock prices reflect all available information.” In the process of ex-
amining the behavior of returns, the finance profession has uncov-
ered many mispricings or inefficiencies where the direction of price
movements is predictable and may suggest the formation of certain
profitable trading strategies.
Unfortunately, much of current academic research in finance is
not accessible to most individual and institutional investors due to
Moreover, academic research usually stops short of suggesting
practical applications. The purpose of this book is to address those
The discussions of the anomalies have two main components.
The first component attempts to make relevant academic research
available in a form that is understandable to practitioners, inves-
tors, students, and academics not in that particular field. It describes
the anomaly, empirical evidence, and possible explanations for the
anomaly, and it explores reasons for the persistence of the anomaly.
The second component of each chapter introduces and implements
trading strategies designed to capture the mispricing, along with a
discussion of the risk and return. In addition, the step-by-step trad-
ing strategy is illustrated with real data from a recent period so that
an ordinary investor would find it easy to duplicate the strategy.
Readers, if they so desire, will be able to further explore literature
on the subject by perusing the extensive bibliography throughout
the book and by possibly conducting additional empirical analysis
This book is intended for any individual interested in mispricings
in the stock market. It does not presume a deep understanding of
financial markets, just an interest in the stock market and a thirst
for knowledge. Investors and practitioners will gain from a sum-
mary of the current research on anomalies and evidence of the suc-
cess of low-risk investment strategies based on those anomalies.
Their trading activities may even make the markets more efficient!
Academics can use the book as a starting point for an understand-
ing of the large field of market efficiency. The references should help
steer the academic community in the right direction to further ex-
plore this exciting and important area of research. The book can
help students at all levels (advanced undergraduates, MBAs, and
PhDs) enhance their understanding of financial markets.
Most but not all anomalies are expected to generate tradable prof-
its. Even if generating trading profits is not possible, information
about an anomaly will help the reader better understand the
mispricing and, perhaps, modify trading behavior to avoid being
hurt by it.
Description of Content
This book begins with a description of market efficiency and anoma-
lies so that readers can fully comprehend the nature of the anoma-
lies discussed. The discussion of market efficiency and its importance
is followed by answers to questions such as: What is mispricing?
How do you detect a mispricing? Is there really a mispricing after
correcting for biases? Why does a mispricing persist? My intent is
for you to be able to judge whether the anomaly is believable and
continues to exist. This is the only chapter that I recommend you
read before reading any other chapter in the book.
The introductory chapter (Chapter 1) is followed by the main part
of the book (Chapters 2 to 11), where ten mispricings are discussed.
Each chapter discusses one anomaly in detail along with the descrip-
tion, evidence, explanations, and risks and rewards of the investment
strategy associated with that anomaly. I have kept each anomaly in-
dependent of the others so that if you are interested in the forward
rate bias, for example, you can jump to Chapter 11 without having to
trudge through the first nine anomalies. The summary at the begin-
ning of each chapter and Table 0.1 allow you to preselect the anoma-
lies that you are interested in reading about. While most anomalies
have seemingly rational explanations related to institutional features,
there are others for which rational explanations have yet to be dis-
covered. Even if an explanation is known to exist, a nagging question
remains: Why doesn’t the mispricing disappear because of the ac-
tions of arbitrageurs or smart investors? That question is frequently
difficult to answer. Limits of arbitrage activity are one possible ex-
planation. Fortunately, trading by individual investors can relax that
constraint, and the investors can gain while making the market more
efficient. I hope this book will enable small investors to uncover and
trade on the mispricings discussed.
A chapter devoted to a discussion of behavioral finance follows
the individual anomalies. Whereas finance theory is based on ratio-
nal investor behavior, behavioral finance theory is based on psy-
chological precepts that generate irrational investor behavior, or at
least behavior that is irrational from an economic standpoint. In the
context of anomalies, the chapter on behavioral finance performs
two functions. First, it provides an alternative way of thinking about
the rationale behind some of the anomalies. Second, it provides use-
ful information about mistakes that investors make, mistakes that
investors should consciously try to avoid.
The last chapter of the book is a collection of other possible
mispricings and is directed to readers whose appetite for anomalies
is not satisfied. The most promising mispricings are described in
that chapter, along with an extensive list of references that allow the
reader to explore beyond the confines of the book.
The three appendices at the end of the book contain useful infor-
mation for people who are new to certain aspects of trading strate-
gies. Appendix Acontains information about financial instruments,
their availability, trading costs, and trading restrictions. The purpose
is to provide practical information on selecting appropriate instru-
ments for trading. Appendix B covers the intricacies of short selling.
Table 0.1: Summary of Anomalies discussed in the book
real time data*
Once a year
One; change in
Once a year
1.5% to 3.0%
One; change in
Not difficult to
1.5% to 3%
30 to 38%
selling only for
Not difficult to
10% per year
1% to 50%
5% to 7%
Easy with funds
difficult to find
7% to 10%
30% to 57%
Changes to the
S&P 500 Index
36% to 48%
Not difficult to
4% to 10%
selling only for
Easy for cash
20 to 100
Not difficult to
2% to 8%
2% to 5%
13% to 15%
*Abnormal return is the return in excess of the normal return associated with this level of risk.
Buying stocks or selling stocks that you own is easy. However, short
selling (selling stocks that you do not own) is a somewhat different
and more complex strategy and is described in that appendix. Ap-
pendix C explains the basics of hedging. Hedging can be used to
control risk associated with certain trading strategies. The appendi-
ces are not required reading for frequent traders.
Why Did I Write This Book?
If stock market experts were so expert, they would
be buying stock, not selling advice.
Norman R. Augustine
I share the skepticism of this statement and agree with the asser-
tion that any person will use his informed position to make profits
for himself first. However, the statement implicitly assumes that stra-
tegic trading will generate arbitrage profits that have no risk and re-
quire no investment. Unfortunately, arbitrage is rarely risk free or
costless (see next chapter for an in-depth discussion on the limits of
arbitrage). So, although I have the knowledge, the ability, and the will-
ingness to craft an informed trading strategy that outperforms the
market, I am constrained by the lack of adequate financial resources
(I am only a professor of finance after all!) to take advantage of the
many profitable opportunities that I discuss in this book.
Not to say that I have not profited from my expertise—as a small
investor I have implemented, and continue to implement the strat-
egies in this book—generally, managing to beat the market and make
the desired level of profit. Yet, due to the resource constraint men-
tioned above, it is more profitable for me, both personally and pro-
fessionally, to leverage my know-how in the form of this book, than
to try and earn direct profits through the implementation of the strat-
egies I have highlighted in the pages that follow.
In one sense then, this book itself can be treated as an anomaly
(considering the above quotation), which, if fully exploited by its
audience, would help to push the market back to its ideal of effi-
ciency. This is another reason why I am writing this book instead of
using my knowledge only for personal benefit.
1. Both quotes in this paragraph are from the August 2001 issue of the Institu-
tional Investor, 30–33.
I would like to acknowledge with great appreciation the support
and encouragement of Art Keown. As editor of the Financial Man-
agement Association Survey and Synthesis series, author of many
books, and a colleague, Art facilitated the approval of this idea by
the Financial ManagementAssociation’s Survey and Synthesis Board
and the publisher. He has also been an active participant in various
stages of the project, a constant source of encouragement and help,
and a sounding board, for which I am extremely grateful.
Paul Donnelly, executive editor of finance at Oxford University
Press, has been a strong believer in this book from the start and has
been instrumental in its quick acceptance at all levels. He has helped
me write this book for the right audience and provided continuous
feedback and encouragement in this endeavor. I owe him a debt of
I would like to express my sincere appreciation to the editorial,
production, and marketing groups at Oxford University Press for
doing an outstanding job in producing a high quality product that
reaches as many potential interested readers as possible. In particu-
lar, my thanks go to Helen Mules, Woody Gilmartin, and Sue Warga.
I thank the reviewers of this book, who worked hard to tell me
what was missing and what needed more work. In particular, I
would like to acknowledge the help of Rakesh Bali of Adelphi Uni-
versity, Dan Strachman of Answers and Company, Will Glasgow
of U.S. Trust, Mahesh Pritamani of Frank Russell and Co., Venkat
Ramaswamy HSBC, Bhoopat Jadeja of Tibco, and Harry Larsen of
Finally, and most importantly, I appreciate the work put in by
committed individuals who read the book in its entirety and pro-
vided detailed feedback. They include MBA students Stephen
Deutsch, Virginia Benczik, Wes Gatewood, Huanmin Xu, Ajay
Bhootra, and Robert Ratcliff and doctoral students Tunde Kovacs
and Don Autore at Virginia Tech, Prasad Polamraju of Celanese
Hoechst, Professors Dilip Shome and Randy Billingsley of Virginia
Tech, Kathy Sevebeck of K&B Designs, and especially, Sonia
Mudbhatkal of Virginia Tech.
BEYOND THE RANDOM WALK
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This chapter addresses common questions related to market efficiency
and anomalies. If prices properly reflect available information, then
markets are said to be efficient. Although markets are known to be
broadly efficient, there may be pockets of inefficiency that lead to
mispricings or anomalies.
In general, claims of anomalous pricing must be viewed with skepti-
cism. The discussion describes reasons for skepticism as well as causes
for persistence of some anomalies. Moreover, even when profits can’t
be made by trading on anomalous prices, it may be possible to alter
trading behavior to avoid losses due to these anomalies.
What Is Market Efficiency?
Market efficiency in this book refers to the informational efficiency of
markets as opposed to structural efficiency, administrative efficiency,
or operational efficiency. That is, this chapter focuses on the effi-
ciency with which information is reflected in prices. If new infor-
mation becomes available about a stock (change in earnings), an
industry (change in demand), or the economy (change in expected
growth), an efficient market will reflect that information in a few
minutes, even a few seconds. However, if only half of that informa-
tion is reflected in the stock price immediately and the remaining
half takes several days, then the market is less than fully efficient.
Markets that are less than fully efficient open an opportunity for
making profits because the inefficiency causes a mispricing in stocks.
If a stock is slow to react and takes several days to fully reflect new
Market Efficiency and
Beyond the Random Walk2
information, then buying the stock immediately after good news
and holding it for a few days would generate extra profit. However,
if many people know about this inefficiency, they will all act the
same way. As a result, the price will reflect the new information
more quickly and the inefficiency will eventually disappear.
The idea behind efficient capital markets is quite simple but com-
pelling. If you know that a stock is undervalued, then you will buy
the stock until it is fairly valued. Or if the stock is overvalued, then
you will sell the stock until it is fairly valued. Thus, market partici-
pants will ensure that prices are always accurate based on publicly
The implicit assumption here is that trading
based on nonpublic information, that is, insider trading, is illegal.
Markets are said to be “semi-strong” form efficient if the prices are
unbiased based on all publicly available information. If prices are
unbiased based on all information (public and private), then mar-
kets are “strong” form efficient. Empirical evidence suggests that
markets in the United States and other developed countries are es-
sentially informationally efficient in the semi-strong form, though
pockets of inefficiency may exist.
Who Cares about Market Efficiency?
Market efficiency is important for everyone because markets set
prices. In particular, stock markets set prices for shares of stock.
Currency markets set exchange rates. Commodity markets set prices
of commodities such as wheat and corn. Setting correct prices is
important because prices determine how available resources are
allocated among different uses. If the price of a product is low rela-
tive to its cost, the investment in that product will fall. On the other
hand, high prices encourage a greater allocation of resources. Thus,
correct prices are important for resource allocation and, conse-
quently, for economic growth. Unfortunately, correct prices are im-
possible to achieve because they require perfect foresight and
information. The best a market can do is to form prices that reflect
all available information.
Now, consider market efficiency for each constituent in turn: in-
vestors, companies, the government, and consumers. Investors are
suppliers of capital that companies need for investment and opera-
tions. The investors earn a return on the capital they supply. If in-
vestors find that prices are predictable, then smart investors can
earn extra return at the expense of naive or unsophisticated inves-
tors. This implies that unsophisticated investors earn a return that
Market Efficiency and Anomalies 3
is less than the return that they should receive. In such an environ-
ment, unsophisticated investors will be reluctant to supply capital.
The reduction in the availability of capital means that companies
must pay a higher return for the capital due to restricted supply.
However, the investors’ capital does not disappear from the market
altogether. The money not invested in corporate securities may be
deposited with financial institutions, which may then lend that
money to corporations. However, the cost of that money will be
higher than if the companies could borrow directly from investors.
Besides the cost implication, companies care about market effi-
ciency in another way. If markets are efficient aggregators of infor-
mation, then companies can learn from the stock price reaction. For
example, when AT&T bid for NCR in December 1990, AT&T’s stock
price promptly fell more than 6 percent, while NCR’s price jumped
44 percent. Robert Allen, AT&T chairman, chided the markets for
not appreciating the long-term benefits that would accrue to AT&T
as a result of this combination. It took five years, but the market
was proven right. AT&T bought NCR for $7.48 billion in 1991 but,
after losses totaling $3.85 billion over the next five years, it was forced
to spin off NCR in 1996 at less than half the purchase price, about
$3.5 billion. Most companies, however, listen to the market’s ver-
dict on big decisions. Some mergers are aborted because of tepid
reception by the market.
In addition to investors and companies, the government and the
public are concerned about market efficiency because of the effect
on economic growth. If the markets do not set prices based on all
available information, then allocation of resources based on market
prices will be flawed. Industries that deserve more capital will not
get that capital, while industries that are not deserving of greater in-
vestment will. For example, if technology companies are overvalued
by the market, then too many resources will be invested in technol-
ogy companies, resulting in a misallocation.Also, market inefficiency
in the form of speculative bubbles can affect the financial institu-
tions and, through them, the entire economy. For example, Japan’s
stock market and real estate bubble in the 1980s has left the Japa-
nese banking sector with nonperforming assets, affecting the
Improper utilization of limited capital means
suboptimal use of funds and underachievement in terms of growth
and social welfare. Under such conditions, it is the government’s
responsibility and duty to intervene in financial markets to ensure
optimal resource allocation. Whether the government can achieve
the desired effect is an open question.
Beyond the Random Walk4
Thus, market efficiency is important so that optimal investment
ensures optimal growth and maximizes social welfare.
Can Capital Markets Be Fully Efficient?
While market efficiency is desirable, there are three limitations in
achieving that ideal: the cost of information, the cost of trading, and
the limits of arbitrage. Strictly speaking, arbitrage refers to a profit
earned with zero risk and zero investment. However, in this book
the term is used in its more popular interpretation, that is, a supe-
rior risk-return trade-off that probably requires both risk and in-
LIMITATION 1: COST OF INFORMATION
In an article aptly titled “On the Impossibility of Informationally
Efficient Markets,” Sandy Grossman and Joe Stiglitz go about prov-
ing just that. The concept behind the impossibility of informationally
efficient markets is straightforward. Let us assume that markets are
fully efficient, that is, they instantaneously reflect new information
in prices. If that is the case, then no investor or market participant
has any incentive to generate or report new information because
the value of that information is zero. That is, when a company an-
nounces its earnings, no one wastes time trying to analyze that in-
formation because the price already reflects it. There is no value in
even reading the corporate announcement. But if no one has any
incentive to react to new information, then it is impossible to reflect
new information in prices.
The implication of this is that markets can’t be fully efficient be-
cause no one has the incentive to make them so. Market participants
must be compensated in some way for making the market more effi-
cient. Arbitrageurs and speculators must get something in return.
Thus, instead of achieving instantaneous adjustment to new infor-
mation, prices can adjust to new information only with a time lag.
This time lag allows market participants to earn a reasonable return
on their cost of obtaining and processing the information. If the re-
turn is abnormally high, it will attract more information processors,
leading to a reduction in time lag. The net result is that prices take
time to reflect new information because obtaining and processing that
information is costly. However, if the delay is short enough (a few
minutes), the markets are still considered efficient. But if they take
several hours or several days, then the markets are not efficient.
Market Efficiency and Anomalies 5
LIMITATION 2: COST OF TRADING
Like the cost of information, traders incur costs while trading: their
time, brokerage costs, and other related costs (see Appendix A for a
discussion). When the cost of trading is high, financial assets are
likely to remain mispriced for longer periods than when the cost of
trading is low. In essence, like with the cost of information, the
arbitrageurs or other traders must get an adequate return after ac-
counting for costs to engage in an activity that makes the market
more efficient. To the extent that trading activity is limited, prices
will not reflect all available information. One factor that can have a
large influence on prices is the difficulty in short selling. If short
selling (that is, selling a stock that you do not own) is more difficult
than buying long (that is, buying a stock that you do not own), then
prices are likely to be biased upward. And if certain stocks are more
difficult (and therefore more costly) to short-sell, the upward bias
in prices is likely to be greater for those stocks. Thus, the greater the
cost of trading, the greater the mispricing.
LIMITATION 3: LIMITS OF ARBITRAGE
The above discussion on why markets should be efficient suggests
the presence of investors who would trade if they see a price that is
inconsistent with their information, and would continue to trade
until the price reflects the information they have available. On a
simpler scale, consider two financial assets (say, stocks X and Y)
that are equally risky but generate different returns. Obviously, one
of the two assets is mispriced. If asset X generates the higher return
and has a lower price, while asset Y generates the lower return and
has a higher price, then to take advantage of the mispricing,
arbitrageurs would buy asset X while at the same time short-selling
Y. With the activities of like-minded arbitrageurs, the prices will
converge and make them reflect the fundamental value associated
with each asset.
There are four problems with this ideal scenario, however. First,
it is not clear when, if ever, the prices will return to equilibrium
levels or when the mispricing will disappear. If uninformed traders
can continue to influence prices, then the prices of X and Y may
actually diverge even more before eventually converging. If the di-
vergence is significant, arbitrageurs may be forced to close their
positions prematurely. Arbitrageurs who took short positions in
Internet stocks in 1998 or 1999 on the belief that the stocks were
overvalued would have been wiped out before the prices eventu-
ally fell. In fact, many short sellers went bankrupt in the late 1990s
Beyond the Random Walk6
due to the ascent of the stock market. Even Warren Buffett, whom
many regard as a smart investor, proclaimed that he had misread
the new economy by not riding the technology wave. Today we
know that he was correct to be skeptical of high Internet stock valu-
ations, but at the time the prolonged period over which the
mispricing seemed to persist caused him to accept defeat.
Second, it is rare to find two assets with exactly the same risk.
Assume that X gives a higher return because it has a slightly higher
risk than Y. However, smart investors believe that X’s return is much
higher than it should be based on differences in risk. Accordingly,
they would like to implement a strategy of buying X while short-
selling Y. But the risk inherent in such a strategy may deter them
from arbitraging the mispricing. Thus, in cases where no close sub-
stitutes are available, the mispricing of a security may continue in-
Third and probably more important, we implicitly assumed that
arbitrageurs have an unlimited amount of capital to take advantage
of mispriced assets. That is not true. Just like everyone else,
arbitrageurs have a limited amount of capital, which they devote to
the most profitable strategies or to the most egregious mispricings
while ignoring the remaining mispricings. The problem of limited
capital becomes more severe in a bull market. Though there are
potentially more mispricings in a bull market, the arbitrage capital
is even more limited because most investors want to ride the mar-
ket rather than find nebulous mispricings that generate relatively
Finally, most arbitrageurs act as agents because they manage other
people’s money. As agents, arbitrageurs must abide by the con-
straints imposed on them by the owners of capital (the principals).
The principals are unwilling to give the agents a free hand in the
pursuit of extra returns because the principals are concerned that
the agents may not actually earn those extra returns and that the
risk associated with those returns may be unacceptably high. There-
fore, the typical mandate given to an agent will specify permitted
strategies, the amount of capital at risk including the effects of le-
verage, and the maximum possible loss. For example, an arbitrageur
may be allowed to invest only in merger arbitrage securities or only
in distressed securities, with loss limited to 10 percent of the capital
invested. While these constraints protect the owners of capital, they
also limit the operation of arbitrage activities in the market. In addi-
tion, an arbitrageur’s ability to attract more capital can be severely
constrained when opportunities become more attractive if princi-
pals use an arbitrageur’s past performance to judge his ability. As-
Market Efficiency and Anomalies 7
sume that an arbitrageur believes that a stock is undervalued by 10
percent and buys that stock. Assume further that the mispricing
gets worse over the next few weeks and the stock becomes under-
valued by 20 percent. The arbitrageur should probably increase his
stake in the stock. However, in the meantime, due to the worsening
mispricing, the arbitrageur has lost 10 percent of the capital. Princi-
pals observe the loss of 10 percent and may not believe that the
arbitrageur has any superior skills. Instead of giving him or her
more capital, they may ask the arbitrageur to immediately sell that
stock, further depressing the stock price and making the mispricing
even more acute. It is easy to see that there are serious limits of
arbitrage activity that may cause mispricings to persist.
What about the small investor? Why can’t the millions of small
investors seek out and trade on these mispricings, especially the
small mispricings that are ignored by professional arbitrageurs or
where arbitrage activity is limited by constraints imposed on the
arbitrageur? In general, the small investors do not have the exper-
tise and knowledge to identify and profitably trade mispricings. If
this book is able to educate investors so that they trade away the
mispricings or trade in a more rational manner, the markets will
become more efficient aggregators of information, with concurrent
improvement in social welfare.
What Is a Pricing Anomaly?
A mispricing is any predictable deviation from a normal or expected
return. For example, assume that IBM’s stock is expected to earn a
normal return of 15 percent a year. If the current stock price is $100,
then the price should increase to $115 after one year, assuming that
IBM does not distribute any dividends. If a market timer predicts that
IBM will actually appreciate by 20 percent or more this year, and IBM
does earn more than the normal return repeatedly and consistently
in a predictable manner, then it is a mispricing. Similarly, a predictable
deviation on the downside (less than 15 percent) is also a mispricing.
On the other hand, an unpredictable movement in price is not a
mispricing. For example, if the actual price after a year is $90 or $130,
that is not a mispricing even though the actual return is different from
the expected return. Deviations from the normal return are expected
and, by definition, must occur for risky securities. On average, how-
ever, the deviation must be close to zero.
If a mispricing is well known and persistent, then it is referred to
as an anomaly. In their article on anomalies in the Review of Financial
Beyond the Random Walk8
Studies, Michael Brennan of UCLA and Yihong Xia of the Univer-
sity of Pennsylvania define an anomaly as “a statistically signifi-
cant difference between the realized average returns . . . and the
returns that are predicted by a particular asset pricing model.” Thus,
persistent realization of abnormal returns (actual return minus the
expected return) is referred to as an anomaly. The persistence in
abnormal returns results in predictability of returns.
When Is a Mispricing Not a Mispricing?
Investment professionals, academics, and novice traders spend a
great deal of time and effort to discover mispricings because these
phenomena have the potential to make someone very rich. There-
fore, mispricings are frequently touted by market timers, brokers,
and other investment professionals. It is important to know how to
judge the validity of a mispricing. In this section, the limitations
and biases in the process of discovering mispricings are discussed
along with simple tests to detect whether the mispricings can be
attributed to such limitations. An understanding of these biases can
be used to test other mispricings. Moreover, it will be natural to
become more skeptical of mispricings or anomalies that are fre-
quently cited as evidence against market efficiency. The intent here
is not to actually check for limitations of the mispricing, but to judge
whether flaws in the discovery process may have caused the ob-
MEASUREMENT OF ABNORMAL RETURN
If markets are efficient, then the expected abnormal return is zero.
On the other hand, if the abnormal return is nonzero and it is pos-
sible to predict the direction of the deviation, then the pricing con-
stitutes an anomaly. Since abnormal return is the actual return minus
the normal return, a problem arises in defining the normal return
(the term is used interchangeably with expected return). How do you
define or measure normal return?
In the IBM example, it was assumed that the normal return is 15
percent. Is the 15 percent assumption correct? Who can say? Unfor-
tunately, there is no accepted method for estimating a stock’s nor-
mal return. Theoretical models include Nobel laureate William
Sharpe’s capital asset pricing model (CAPM) and Steve Ross’s arbi-
trage pricing theory (APT). APT cannot be applied in a practical
way because there are too many unknowns. CAPM is determinis-
Market Efficiency and Anomalies 9
tic, but the CAPM does not have much empirical support. In the words
of Eugene Fama, “[I]nferences about market efficiency can be sensi-
tive to the assumed model for expected returns” (Fama 1998, 288).
Other models exist using alternate measures of risk derived from
statistical methods and historical returns. Researchers have also dis-
covered that stock return depends on such factors as size, the ratio
of market value to book value, beta, momentum, and so on. How-
ever, these are empirical returns that do not necessarily have strong
theoretical support. Further, there is no guarantee that these factors
will continue to have explanatory power in the future. So, the ques-
tion remains: what is IBM’s normal return? There is no exact and
generally accepted measure of expected return. However, it is pos-
sible to say that a particular return is too high or too low. For ex-
ample, a normal return of 50 percent for IBM is too high and a return
of 0 percent is probably too low. One way of getting a reasonable
estimate is to estimate its relative return—relative to another firm
with similar characteristics. The idea is to identify a similar (or con-
trol) firm—similar on several dimensions known to explain the cross
section of returns, such as size, market-to-book ratio, and so on.
Then measure the abnormal return for the sample firm as the differ-
ence between the sample firm’s return and the control firm’s re-
turn. Coke and Pepsi are good examples. If Coke and Pepsi are
considered similar firms, then to find Coke’s abnormal return,
Pepsi’s return would be used as the normal return. The difference
between Coke’s actual return and Pepsi’s return is the abnormal
return earned by Coke. Generally, it is better to use a group of firms
as a control instead of using a single control firm so that one firm’s
chaotic price movements don’t significantly influence the abnor-
mal return calculation.
How critical is it to estimate IBM’s normal return accurately for
detecting a mispricing? Should it be 15 percent or 25 percent per
year? The normal return becomes crucial only in long-term
mispricings. Consider that IBM’s return based on a particular
mispricing is 25 percent over one year. The return is abnormal if the
normal annual return is assumed to be 15 percent, but not if the
normal annual return is 25 percent. On the other hand, if the
mispricing occurs over short periods of time, then the normal re-
turn becomes essentially inconsequential. If IBM’s stock earns 1
percent in a day, then the normal return does not really matter—
whether it is 0.06 percent per day (15 percent per year based on 250
trading days per year) or 0.1 percent per day (25 percent per year).
In either case, the mispricing is large: 0.94 percent or 0.90 percent
for a day. This means that, holding the magnitude of mispricing
Beyond the Random Walk10
constant, long-term mispricings should generally be subject to a
much greater degree of skepticism than short-term mispricings.
As Fama states, “[A]n advantage of this approach [short-period
event studies] is that because daily expected returns are close to zero,
the model for expected returns does not have a big effect on infer-
the problem with long-term normal returns: “the bad-model prob-
lem is ubiquitous, but it is more serious in long-term returns. The
reason is that bad-model errors in expected returns grow faster with
the return horizon than the volatility of returns” (Fama 1998, 285).
If you look hard enough at almost any bunch of numbers, you can
find a pattern. Since anomalies are predictable patterns in returns, a
person who studies hundreds of different relationships and mil-
lions of different observations is likely to find a pattern; this is called
data mining. For example, try to find a relationship between the
stock return and any number of different variables, such as the
weather in New York, the number of sunspots, the height of ocean
waves, growth in world population, or the number of birds in San
Francisco. Given a large enough number of possible relationships
and enough tries, it is possible to find a statistically significant rela-
tionship between a stock return and another variable. That relation-
ship does not really exist: it is there just by chance. Further, as Fama
states, “splashy results get more attention, and this creates an in-
centive to find them” (Fama 1998, 287). Fischer Black once said,
“[M]ost of the so-called anomalies that have plagued the literature
on investments seem likely the result of data-mining” (Fischer Black
An example of data mining is illustrative. Take a researcher who
believes that Nasdaq 100 returns are predictable on an intraday ba-
sis. He is determined to find this predictability to impress his boss.
He can generate and test for thousands of different relationships to
discover a pattern. He begins by calculating the six one-hour re-
turns for each day: 10 A.M.–11 A.M. return, 11 A.M.–12 noon return,
and so on. He analyzes the hourly returns to see whether the return
during the first hour is related to the return during the second hour,
whether the second-hour return is related to the return during the
third hour, and so on. Then he tries to find significant correlations
among 13 half-hour returns, and among 26 quarter-hour returns,
and among 78 five-minute returns, and among 390 one-minute re-
turns. Unsuccessful but persistent, he introduces filters, that is, se-
Market Efficiency and Anomalies 11
lects only those observations where the Nasdaq 100 return is more
than two standard deviations away from the mean. Again he fails
to discover anything interesting. Next he introduces volume as a
variable. Only those observations that have trading volume in the
top 10 percent are selected. He continues this process until he dis-
covers a pattern. Finally he finds that on high-volume days, a nega-
tive Nasdaq 100 return in the 3:00–3:30 P.M. period is followed by a
negative return in the 3:30–4:00 P.M. period with a 90 percent prob-
ability. This is data mining at its best, but the boss is not impressed,
and I hope you are not either.
Artificial anomalies need to be separated from real anomalies.
Perhaps the most important thing is to assess the intuitiveness of
the relationship discovered by researchers. Does it make sense? Can
the number of birds in San Francisco really mean anything for stock
returns? If it doesn’t make intuitive and economic sense, then it is
probably a case of data mining. Another way to check for data min-
ing is to use an out-of-sample test, which is testing the same rela-
tionship using data from a different country or for an entirely
different period. If data mining worked in this case, it may not work
for a different sample. If it is not possible to get another data set,
then test the relationship over subperiods of the data. The results
must hold for subperiods as well as for the whole period unless
there is a valid reason for a change in the observed relationship.
Another source of unreliability of an anomaly is survivorship bias,
which exists whenever results are based on existing entities. For
example, a simple study of existing mutual funds will find that
mutual funds, on average, outperform their benchmarks. The prob-
lem with such a sample is survivorship. Only well-performing funds
continue to survive, while the underperformers die. Thus, a sample
of existing mutual funds will not contain funds that underperformed
and died. If all funds, dead and alive, are included in the sample,
then the funds, on average, do not outperform their benchmarks.
The sample of existing mutual funds has a survivorship bias and
will result in an overestimation of fund performance.
Survivorship is important in market timing studies, as market
timing newsletters or services use many strategies and frequently
add new strategies and discontinue others. Which ones does the
market timer add? The ones that have shown great promise based
on past trends. Which ones are discontinued? The ones that no longer
show continuing profitability. The record displayed by the market
Beyond the Random Walk12
timer shows only the successful strategies and not the unsuccessful
strategies, giving readers the false impression of market timing
prowess where none exists.
Survivorship bias is widespread in many spheres of the invest-
ment world. People with a good investment record are retained, while
others are dumped. It seems as if all the investment firms have ana-
lysts who can predict the market. What about the guests on CNBC?
Are they really good stock pickers, or are they simply lucky?
SMALL SAMPLE BIAS
Mispricings may be caused by a small sample bias. Usually the small
sample refers to the period of observation. For example, riskier stocks
should earn higher returns than other stocks. Since stocks with small
market capitalization (size) are considered riskier than large-size
stocks, small-size stocks are expected to earn higher returns. How-
ever, during the 1995–99 period, the large-size stocks outperformed
the small-size stocks. Looking at this limited time period, one may
conclude that a mispricing exists. However, over long periods (1926–
2002 or 1962–2002) small-size stocks did earn higher returns than
large-size stocks. The small sample bias is especially relevant to
anomalies that do not have a reasonable explanation, especially if it
appears that the mispricing has occurred just by chance.
Another bias that may creep into the discovery of mispricings is se-
lection bias, that is, the sample may be biased in favor of finding the
desired result. Assume you want to measure the ownership of cell
phones in the generalAmerican population. If you polled only people
working in Manhattan, your estimate will be biased upward because
the sample is biased and the result is falsely attributed to the entire
American population, including rural and less urban areas.
In the case of stock market studies, a selection bias can creep in
when the results arise from a certain part of the sample but seem to
be representative of the entire market. For example, consider the
January effect. According to the January effect, firms gain abnor-
mally in the first few days of January. However, the effect is not
broad-based; rather, it is due to firms that are small in size. Once the
small firms are removed, the January effect disappears. The discov-
ery of the small-firm effect is important, because it is necessary to
attribute the effect to only the small firms and not to the entire stock
Market Efficiency and Anomalies 13
Stocks trade with different frequencies. Some stocks may trade
continuously, that is, several times a minute, such as Pfizer, Intel,
and Cisco. Other stocks may not trade for several hours or even
several days. If a stock trades only once every day, at 10 A.M., the
return based on that day’s 10 A.M. trade will capture market move-
ments that took place over the last twenty-four hours. The closing
price at 4:00 P.M. will reflect the price of the last trade, which actu-
ally took place at 10 A.M., without accounting for any market move-
ments that have taken place since 10 A.M. If the market jumped after
10 A.M., then the next day’s return (but not today’s return) of this
stock will reflect the increase in price. If you construct a portfolio of
such inactively traded stocks, then it will seem that these stocks
have predictable returns—that is, the stock price will change in ac-
cordance with the market, but with a delay. Since you can predict
returns, a natural strategy is to buy this portfolio whenever the
market goes up after 10 A.M. and sell this portfolio if the market
goes down after 10 A.M. The problem with returns caused by
nonsynchronous trading is that those returns are not actually trad-
able. The 10 A.M. price is not a price at which a trade can be ex-
ecuted. As soon as any trader tries to trade, the price will move to
reflect market movements, and the excess returns will disappear.
There is a way to take advantage of stocks that trade infrequently
or at different times: trade mutual funds, where a buy does not nec-
essarily trigger a trade in the underlying stock. Those cases are dis-
cussed in Chapter 6, “Mispricing of Mutual Funds.”
Most investors demand a higher return for a riskier position than
for a less risky position. That is why bank deposits give a lower
return than stocks, because stocks are riskier than bank deposits.
Small-size stocks have higher returns than large stocks because small
stocks are riskier than large stocks. This means that a riskier strat-
egy must also generate a higher return. Therefore, it is important to
control for risk when comparing trading strategies designed to take
advantage of mispricings. Further, historical risk estimates may not
be appropriate if the mispricing is around certain corporate or mar-
ket events, because volatility, and hence risk, generally increases
around those events. Thus, anomalies that are event-driven must
generate higher returns to compensate for the risk associated with
those events. However, risk is probably not important if only a short
holding period is required.
Beyond the Random Walk14
In any case, the abnormal returns computed for any mispricing
must account for the level of risk inherent in exploiting that anomaly.
Inaccurate estimates of risk are more likely to affect anomalies that
require long holding periods or anomalies that have very small ab-
normal returns even with short holding periods. Therefore, care must
be taken to ensure that adequate compensation is provided for risk.
EXPLANATION FOR THE MISPRICING
It is necessary to reiterate the importance of a reasonable and intui-
tive explanation as a basis for the anomaly. Anomalies that are based
on reasonable explanations are less likely to be the figment of
someone’s imagination or data mining and are more credible. Some
anomalies exist because of government regulations or arise from
institutional constraints. For example, the January effect is best ex-
plained by capital gains taxes. That is not to say that all anomalies
must have rational explanations. However, an anomaly with a ra-
tional explanation is more believable than one without.
Can New Mispricings Be Discovered?
Until now, the discussion has focused on known anomalies. But
investors, academics, and practitioners are constantly trying to dis-
cover new mispricings. Any new mispricing can potentially result
in large profits to the explorer. While one must be skeptical of new
mispricings—whether it is predicting when a stock split will be
announced or which firm will be acquired—one must acknowledge
the possibility of discovering new mispricings. Just because a pat-
tern can’t be discovered may not mean that it doesn’t exist. At the
same time, one must be wary of new mispricings and ensure that
they meet the tests listed above.
Why Does a Mispricing Persist?
If a mispricing exists, then smart investors and arbitrageurs should
take advantage of it to earn abnormal returns. As more and more
arbitrageurs participate, the mispricing should disappear. In gen-
eral, persistence of an anomaly is a cause for concern. However,
there could be a number of reasons for an anomaly’s continuation,
as discussed below.
Market Efficiency and Anomalies 15
THE MISPRICING IS NOT WELL UNDERSTOOD
It is possible that a mispricing is well known but not well under-
stood. For example, the weekend effect is well known. According to
the weekend effect, first discovered in the 1970s, the return on the
last trading day of the week is highly positive. On the other hand,
the return on the first trading day of the week is usually negative.
Until recently the weekend effect did not have a good explanation.
Without a satisfactory and intuitive explanation, the mispricing does
not meet one of the key conditions for acceptance. Though there is
overwhelming evidence of its existence based on past data, inves-
tors are wary of trading on it because the mispricing may cease to
exist at any time or may not occur during the current period. As
Gabriel Hawawini and Donald Keim remark, “[that] effects have
persisted for nearly 100 years in no way guarantees their persis-
tence in the future” (Hawawini and Keim, 2000, 35).
Further, without knowledge of a reason, it is difficult to identify
stocks that will exhibit the mispricing. Is it only among small stocks?
Is it among large stocks? Is it among stocks that have listed options?
Or maybe among stocks that just issued new equity? It becomes
very risky for an arbitrageur to try to profit from a mispricing with-
out knowing why it exists. As a consequence, the mispricing may
not be arbitraged by risk-averse investors.
ARBITRAGE IS TOO COSTLY
Sometimes the anomaly is known and understood but the arbitrage
is too costly to transact. These costs have three components. The
first component is the bid-ask spread, which is the difference be-
tween the highest price that any buyer is willing to pay (the bid
price) and the lowest price that a seller wants (the asking price). As
all arbitrage strategies require a buy and a sell, the spread contrib-
utes to the total cost of transacting. Second, brokerage fees must be
paid. Finally, each large trade can have a market impact. Even an
actively traded stock such as General Electric may find it difficult to
absorb a million-share order without moving the price. A large buy
will cause the price to rise, meaning you pay more than the price
indicated by the quotes. Similarly, a large sell will cause the price to
decline. In both cases, the market impact of the order has the effect
of increasing the trading costs.
Anomalies with high transactions costs may persist because large
institutions or arbitrageurs may be reluctant to trade if large dollar
positions cannot be taken without moving the price or if the bid-ask
spreads are large. For example, the January effect has been known
Beyond the Random Walk16
for decades and is caused by tax-loss selling of small-size stocks.
Nonetheless, the January effect persists because it is necessary to
trade hundreds of small-size stocks. Small stocks have high bid-ask
spreads and low liquidity, making the potential benefit insufficient
to offset the transaction costs.
PROFIT POTENTIAL IS INSUFFICIENT
Certain anomalies may generate small profits that cannot be multi-
plied easily. In those cases, institutions may not be interested be-
cause there is a limited profit potential. Imagine a $1 billion mutual
fund trying to make a profit of $10,000 on a few trades. The return is
only 0.001 percent. The fund manager could probably spend time
more profitably on other pursuits. This is especially true of trading
in small-cap stocks, where the institutions can’t take large positions
for fear of moving the price. Such mispricings are ideally suited to
ARBITRAGE IS NOT POSSIBLE DUE TO TRADING RESTRICTIONS
A known mispricing may persist if institutional features limit trad-
ing. This is especially true for restrictions on short selling. For ex-
ample, it is not possible to short-sell initial public offerings (IPOs)
for a few days after the issue because shares are not available to
borrow. The mispricing, if any, may persist for a few days, until
short selling becomes possible. Again in the case of IPOs, the un-
derwriters engage in price stabilization activities that can, in some
cases, keep the price at an inflated level for almost a month.
A case in point is the spin-off of Palm by 3Com. 3Com sold a
fraction of Palm as an IPO in March 2000 but retained 95 percent of
its shares. At that time it announced that it would spin off the re-
maining shares to 3Com shareholders at the rate of 1.5 Palm shares
for every 3Com share. Even assuming that 3Com was worthless
without Palm, 3Com’s share price should have been approximately
1.5 times Palm’s share price because a single 3Com share gave the
right to own 1.5 Palm shares. On the first trading day after the IPO,
Palm’s price was $95. Using the ratio of 1.5:1, 3Com’s price should
have been about $142.50. However, 3Com’s price was only $82. A
simple strategy to earn an arbitrage profit would have been to buy
1 share of 3Com and short-sell 1.5 shares of Palm. But arbitrageurs
could not employ this strategy because shares of Palm were not
available to short-sell. In this case, the mispricing existed, and per-
sisted for several days, because of trading restrictions.
Market Efficiency and Anomalies 17
BEHAVIORAL BIASES MAY AFFECT INVESTMENT DECISIONS
If investors are reluctant to realize losses, are quick to take profits,
do not diversify enough, and suffer from other instances of irratio-
nal behavior, then mispricings may occur. They may persist because
investors do not change their behavior even in light of new infor-
mation. The behavioral biases and the manner in which they affect
investment decisions are discussed in Chapter 12.
Underreaction to earnings news can be explained by behavioral
biases. If the earnings announcement is positive, the stock price rises.
But the rise is stymied by the premature selling initiated by indi-
vidual investors who sell to realize gains. As the selling pressure
abates, the stock price slowly rises to the correct level. On the other
hand, if the earnings announcement is negative, the stock price falls.
But it does not fall sufficiently because individual investors con-
tinue to hold on to the stock hoping to recoup their losses. The stock
eventually reaches the correct price but with a delay due to the be-
havioral biases of the investors.
However, irrational investor behavior can explain persistence only
in conjunction with other explanations. Even if some investors are
irrational, arbitrageurs should take advantage of that irrationality
and in the process cause the mispricing to disappear.
Until investors learn to think and act rationally and minimize
emotional trades, mispricings are also likely to be caused by irratio-
LIMITS OF ARBITRAGE REVISITED
One reason for persistence of mispricings is the limits of arbitrage.
As discussed in “Can Capital Markets Be Fully Efficient?” earlier in
this chapter, arbitrageurs may not have the capital or the freedom
to pursue the mispricings as aggressively as they would otherwise.
However, the limits placed on arbitrageurs allow individual inves-
tors to gain from the knowledge provided in this book. If individual
investors begin to target mispricings effectively, there will be one
less reason for the persistence of mispricings in financial markets.
Can Valid Anomalies Be Unprofitable?
menting trading strategies designed to take advantage of mispricings.
Many anomalies are especially suited to individual investors because
the profit potential is small by institutional standards, the mispricing
Beyond the Random Walk18
appears infrequently, or the trading costs are high. Where trading
costs are high, individual investors, like institutional investors, can-
not make arbitrage profits. However, individual investors can alter
the timing of their trades so that they are not negatively affected by
known mispricings. For example, based on the weekend effect, if
an investor wants to sell a stock, he should sell it on a Friday in-
stead of the following Monday.
At the same time, readers must recognize the limitations of this
book and factors that may make these anomalies disappear or ap-
pear not to exist.
DOCUMENTED ANOMALIES ARE BASED ON AVERAGES
Just because an anomaly exists does not mean that all trades will be
profitable. For example, in the case of changes to the S&P 500, stocks
deleted from the S&P 500 index lose value and will usually recoup
their losses within a few weeks. This statement is based on an analy-
sis of over three hundred deletions between 1962 and 2002. Does it
imply that the next stock deleted from the index is likely to appreci-
ate? Yes. But will it appreciate? Maybe not. Similarly, the results do
not imply that the next twenty stocks deleted from the index will
necessarily appreciate, though they are likely to. But the results do
imply that if you follow this strategy for the next two to three years
and no significant changes take place in how the market reacts to these
deletions, then you will earn risk-adjusted returns that are larger than
the normal return. However, an unsuccessful run of any mispricing
can cost the investor a significant loss of capital.
POSITIVE ABNORMAL RETURNS DO NOT MEAN POSITIVE RETURNS
The anomalous evidence presented generally focuses on abnormal
returns. Since an abnormal return is the actual return minus the nor-
mal return, the actual return could be negative even though the ab-
normal return is positive. Consider implementing a trading strategy
with a 10 percent annual abnormal return. If the market drops 23
percent during a year, as it did in 2002, then the actual return is only
–13 percent. Though –13 percent is much better than –23 percent, it is
still a loss. Therefore, the anomalies discussed do not suggest abso-
lute profitability, only profitability relative to the normal return.
CONDITIONS GOVERNING ANOMALIES MAY CHANGE
An anomaly may disappear because of a change in conditions. In
many cases the anomalies exist because of individual or institutional
Market Efficiency and Anomalies 19
reasons. For example, the January and December effects are related
to taxes. If the government reduces the capital gains tax (as in 2003),
then the January and December effects are likely to slightly weaken.
Similarly, it is possible to time mutual funds that hold foreign stocks
because they use stale prices in computing net asset values (see
Chapter 6). If the fund companies revise their rules for pricing, then
the gains due to timing will disappear.
The foregoing discussion assumes that a valid explanation exists
for each anomaly. That is not always the case. There are anomalies,
such as the home bias, for which no reasonable explanation exists.
Home bias is the tendency of investors to underweight foreign stocks
compared to an optimally diversified portfolio. In other cases, the
explanation, though supported by empirical evidence, may be in-
correct. Whenever explanations are either false or unavailable, the
anomaly is likely to disappear without any warning.
ANOMALIES MAY BE ARBITRAGED AWAY BY TRADING
If markets are efficient and investors are rational, then the more
popular this book becomes, the greater the chance that people will
trade on these anomalies until they are no longer profitable. To profit
from this book, however, it is not necessary to trade on the anoma-
lies listed. The primary objective is to ensure an understanding of
these anomalies so that investors can sidestep unprofitable situa-
tions or marginally alter their trading patterns in beneficial ways.
Role of Individual Investors
The fact that the market cannot be fully efficient in spite of the per-
sonal profit motive and the presence of arbitrageurs and other smart
investors provides the basis for this book. As noted above, con-
straints placed on arbitrageurs allow many mispricings to continue.
On the other hand, individual investors are free to invest and trade in
any way they want, with few constraints. Unlike professional
arbitrageurs, individuals can continually change the strategy they
use. Trades of individual investors will not have a significant effect
on price. Aprofit of $5,000 on a few trades is sufficient to compensate
individuals for their time and effort. Individuals can design and imple-
ment an exit strategy by using limit orders and stop limit orders (see
Chapter 12). Arbitrageurs are loath to take on very risky positions.
They prefer small margins but work with very high volume. As a
result, currency markets and bond markets attract significantly more
Beyond the Random Walk20
arbitrage activity than stock markets. Stock markets can be more
effectively tapped by individual investors.
Why aren’t individual investors more active in arbitraging
mispricings? The primary reason is that their knowledge of anoma-
lies is limited. The purpose of this book is to identify anomalies and
make them accessible to investors, professionals, and academics.3
hope that trading based on these anomalies will improve market
efficiency with the associated benefits of superior resource alloca-
tion and enhanced social welfare.
• Markets are said to be efficient if publicly available informa-
tion is reflected in prices in an unbiased manner.
• Efficient markets are desirable for the society because prices
determine allocation of resources.
• Markets cannot be fully efficient because of the cost of collect-
ing and analyzing information, cost of trading, and limits on
the capital available to arbitrageurs.
• All anomalies must be viewed with caution and skepticism, as
spurious mispricings can surface for a variety of reasons, such
as errors in defining normal return, data mining, survivorship
bias, small sample bias, selection bias, nonsynchronous trad-
ing, and misestimation of risk.
• Though anomalies should disappear in an efficient market, they
may persist because they are not well understood, arbitrage is
too costly, the profit potential is insufficient, trading restric-
tions exist, and behavioral biases exist.
• Documented and valid anomalies may still be unprofitable
because the evidence is based on averages (and may include a
large fraction of losers), conditions responsible for the anomaly
may change, and trading by informed investors may cause the
anomaly to disappear.
Market Efficiency and Anomalies 21
References for Further Reading
Alexander, Colin. 1999. Streetsmart Guide to Timing the Stock Market: When to Buy,
Sell, and Sell Short (New York: McGraw-Hill). The author uses basic technical
tools from futures markets to pick stocks.
Black, Fischer. 1993. Return and Beta. Journal of Portfolio Management 20(1), 8–18.
Brennan, Michael, and Yihong Xia. 2001. Assessing Asset Pricing Anomalies. Re-
view of Financial Studies 14(4), 905–42.
Cooper, Michael, Robert Gutierrez, and William Marcum. 2003. On the Predict-
ability of Stock Returns in Real Time. Journal of Business, forthcoming.
Fama, Eugene F. 1998. Market Efficiency, Long-Term Returns, and Behavioral Fi-
nance. Journal of Financial Economics 49(3), 283–306.
Fosback, Norman G. 1976. Stock Market Logic: A Sophisticated Approach to Profits on
Wall Street (Fort Lauderdale: Institute for Econometric Research).
Grossman, Sanford J., and Joseph E. Stiglitz. 1980. On the Impossibility of In-
formationally Efficient Markets. American Economic Review 70(3), 393–408.
Haugen, Robert. 2002. The Inefficient Stock Market: What Pays Off and Why (Upper
Saddle River, N.J.: Prentice Hall).
Hawawini, Gabriel, and Donald B. Keim. 2000. “The Cross-Section of Common
Stock Returns: A Review of the Evidence and Some New Findings.” In Donald
B. Keim and William T. Ziemba, editors, Security Market Imperfections in World-
wide Equity Markets (New York: Cambridge University Press).
Keim, Donald B., and William T. Ziemba (editors). 2000. Security Market Imperfec-
tions in Worldwide Equity Markets (New York: Cambridge University Press).
The book is a collection of academic articles.
Lo, Andrew W., and Craig MacKinlay. 1990. Data Snooping Biases in Tests of Fi-
nancial Asset Pricing Models. Review of Financial Studies 3, 431–67.
——— . 1999. A Non-Random Walk Down Wall Street (Princeton: Princeton Univer-
Malkiel, Burton. 1989. A Random Walk Down Wall Street (New York: Norton).
Michaud, Richard O. 1999. Investment Styles, Market Anomalies, and Global Stock
Selection (Charlottesville, Va.: Research Foundation of the Institute of Char-
tered Financial Analysts). The book focuses on global factor-return relation-
ships for institutional equity management and style analysis.
Noddings, Thomas C. 1985. Low-Risk Strategies for the High-Performance Investor
(Chicago: Probus). This book focuses on convertible bonds.
O’Shaughnessy, James P. 2001. What Works on Wall Street: A Guide to the Best-Per-
forming Strategies of All Time (New York: McGraw-Hill).
Shefrin, Hersh. 2000. Beyond Greed and Fear: Understanding Behavioral Finance and
the Psychology of Investing, Financial Management Association Survey and Syn-
thesis Series (Boston: Harvard Business School Press).
Shleifer, Andrei, and Robert W. Vishny. 1997. The Limits of Arbitrage. Journal of
Finance 52(1), 25–55.
Shleifer, Andrei. 2000. Inefficient Markets: An Introduction to Behavioral Finance (Ox-
ford: Oxford University Press).
Thaler, Richard H. (editor). 1993. Advances in Behavioral Finance (New York: Russell
Beyond the Random Walk22
1. Correct prices are difficult to obtain because it is impossible to predict the
future. However, market efficiency requires only that prices be based on all
2. The government must recognize and respond to the market’s signals. Heizo
Takenaka, Japan’s financial services minister appointed in mid-2002, is the
first “Japanese bank czar who seems sympathetic to the market’s dim view
of the [Japanese] financial system’s health. Mr. Takenaka’s predecessors all
claimed there was nothing wrong with the quality of big banks’ capital—a
claim disputed by the rating agencies. But Mr. Takenaka admits there are
problems. ‘Technically, it’s OK,’ he said in an interview last week. ‘But the
market doesn’t think so.’” Quoted in Phred Dvorak, “Japan’s Financial Cri-
sis Makes a Comeback,” Wall Street Journal, November 22, 2002.
3. Many academics in finance routinely use their knowledge and research to
manage hedge funds or other investment portfolios. For example, Dimen-
sional Fund Advisors, which manages more than $30 billion in assets, is as-
sociated with Eugene Fama of the University of Chicago, Ken French of
Dartmouth College, and two of their former students, David Booth and Rex
Sinquefield. LSV Asset Management, which manages about $8 billion, is
owned by Josef Lakonishok of the University of Illinois, Andrei Shleifer of
Harvard, and Robert Vishny of the University of Chicago. Long Term Capi-
tal Management, whose failure shook world financial markets in 1998 and
which had to be rescued by a group of large banks prodded on by the Federal
Reserve, was advised by Nobel laureates Robert Merton and Myron Scholes.
Small loser stocks are known to appreciate considerably in January,
giving rise to the so-called January effect. The primary explanation for
the January effect is tax-loss selling by investors in December to realize
capital losses that are used to offset capital gains. When the selling
pressure abates in January, the loser stocks appreciate. Unfortunately, it
is not possible to arbitrage the January effect, though investors can gain
by changing their trading patterns.
The December effect is similar in spirit to the January effect. Stocks
that have done well in the January-November period are not sold by
investors in December because selling those stocks will result in tax-
able capital gains. By waiting a few days, investors can postpone pay-
ment of capital gains taxes by almost one year. It is relatively easy to
gain from the December effect, as popularly available indexes can be
used for trading.
Academics, practitioners, and investors have known about the Janu-
ary effect for decades.1
It is generally accepted that the January effect
is a consequence of tax-loss selling. Since investors must pay taxes on
net capital gains, investors sell losers toward year-end to realize capi-
tal losses that can offset capital gains. Thus, past losers experience
abnormal selling pressure in December. In January the selling pres-
sure is relieved, resulting in large gains for loser stocks. Evidence of
large January returns for loser stocks is dubbed the January effect.
Another relatively unknown activity driven by the tax code is
tax-gain selling. If investors realize capital losses to offset capital
The January Effect and
the New December Effect
Beyond the Random Walk24
gains, it is also natural for investors to postpone realization of capital
gains so that they can postpone payment of taxes on capital gains.
Thus, rational investors will sell winners in January instead of De-
cember. By waiting a few days, it is possible to defer payment of taxes
by almost one year. The selling pressure on winners will be small in
December, causing the price of winners to rise. The incidence of large
December returns for winner stocks is called the December effect. The
media sometimes refer to this as the Christmas effect.
DAILY RETURNS BY MONTH
The average daily returns, in percent, by month over the entire 1963–
2001 period are reported in Table 2.1 for all NYSE, AMEX, and
Nasdaq stocks. At the top of the table, equally weighted and value-
weighted returns are reported. Equally weighted return is the mean
return to all stocks, with all stocks carrying equal weights. Value-
weighted return is the mean return to all stocks where each stock’s
weight is equal to its market capitalization. Thus, General Electric’s
return will carry a weight larger than Dell Computer’s because GE’s
market capitalization is larger than Dell’s.
It can be seen from Table 2.1 that, contrary to media reports, the
December return is similar to the return in other months.2
no evidence of a broad-based December rally. The value-weighted
daily return in December is 0.055 percent, compared with 0.070 per-
cent in January and 0.072 percent in November. The returns in April,
August, and October are also at least as large as those in December.
The equally weighted daily return in December is 0.056 percent, the
third lowest among all months, and larger than only the returns in
March and May.
However, the results are different if firms are grouped based on
market capitalization and return. Market capitalization is the mar-
ket value of a firm, computed as the product of the price and num-
ber of shares outstanding. The groups are constructed as follows.
Each month, all firms are categorized into size deciles (ten groups
with the same number of firms in each group) based on the market
capitalization at the end of the previous month from 1963 to 2001.
Within each size decile, return quartiles (four groups with the same
number of firms in each group) are formed based on the price drop
from the maximum price attained over the previous eleven months
to the price at the end of the preceding month. Average daily returns
Table 2.1. Daily Returns by Month
Size Return Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Annual
Equally- 0.101 0.074 0.041 0.070 0.053 0.057 0.056 0.065 0.056 0.061 0.075 0.056 0.065
Value- 0.070 0.048 0.034 0.057 0.047 0.041 0.049 0.055 0.040 0.063 0.072 0.055 0.053
Small Loser Firms
1 1 1.029* 0.192+
0.052 0.025 0.007 –0.050 –0.029 –0.088 –0.050 –0.143+
2 1 0.616* 0.003 –0.050 –0.097 –0.071 –0.130* –0.122+
Large Winner Firms
9 4 0.016 0.052 0.013 0.050 0.013 0.011 –0.008 0.017 0.011 –0.037 0.075+
10 4 0.008 0.043 0.010 0.039 0.012 0.016 0.000 0.011 –0.011 0.002 0.077* 0.090* 0.025*
Returns are reported in percent. Statistical significance is at better than 1 percent for returns marked with * and at better than 5 percent for returns marked with +
Beyond the Random Walk26
in percent are reported for each month in each of the categories.
Firms in the smallest size decile (decile 1) and the lowest return
quartile (quartile 1) within that decile are called small loser firms.
Firms in the largest size decile (decile 10) and the highest return
quartile (quartile 4) within that decile are called large winner firms.
Returns for the next size decile are reported for comparison.
The returns for the select groups are more interesting. On aver-
age, the small loser firms earn significantly positive returns only in
January and February and significantly negative returns in Octo-
ber, November, and December. In fact, the January return is 1 per-
cent per day, a gain of more than 20 percent for January (assuming
twenty to twenty-two trading days per month), compared with a
loss of 4 percent in December. On the other hand, the large winner
firms gain significantly only in November and December. For the
remaining months of the year, the returns are not significantly dif-
ferent from zero. The return in December is about 2 percent for those
firms. For both small loser firms and large winner firms, the differ-
ences between December and January returns are statistically sig-
nificant. The median returns, though not reported, are similar in
magnitude. Also, see the graphs in Figure 2.1 and 2.2.
Besides returns, volume can provide insights into the behavior of
stock prices. The mean daily turnover for small loser stocks is 0.302
Daily Returns by Month for Small Loser firms
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
Figure 2.1 The figure shows the daily returns by month for firms in the smallest
size decile and the lowest return quartile over the 1963–2001 period.
The January Effect and the New December Effect 27
percent in December, which is greater than the turnover in all other
months. In particular, the turnover in January (0.235 percent) is about
20 percent less than the turnover in December for small loser firms.
On the other hand, the December turnover for large winner firms is
among the lowest of all calendar months, while the January turn-
over is among the highest. In contrast to the small loser firms, the
January turnover (0.242 percent) for the large winner firms is about
20 percent more than the December turnover (0.206 percent).
The return and turnover patterns suggest that the small loser firms
and the large winner firms behave differently. The higher returns in
December coupled with higher turnover in January for the large
winner firms are consistent with the December effect. At the same
time, the higher returns in January coupled with higher turnover in
December for the small loser firms are consistent with the January
RETURNS AROUND THE TURN OF THE YEAR
Table 2.1 depicts the returns by month as an aggregate over the en-
tire sample period. In Tables 2.2 and 2.3 you can view the results
from a closer angle: around the turn of the year and by year from
1988 to 2000 (until January 2001). Only the period since the Tax Re-
form Act of 1986 is considered because of tax changes affecting
mutual funds. Under the act, all mutual funds are required to use
Daily Returns by Month for Large Winner Firms
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
Figure 2.2 The figure shows the daily returns by month for firms in the largest size
decile and the highest return quartile over the 1963–2001 period.
Beyond the Random Walk28
October as the end of their tax year. Thus, any year-end tax effect
caused by mutual fund trading has moved from December-January
to October-November. However, the December-January period con-
tinues to be the relevant period for individual investors.
Stocks most likely to experience the January and December ef-
fects are identified by measuring each stock’s drop from the high
price attained during the year to the twelfth last trading day of the
year (roughly the middle of December). Winners are defined as
stocks in the smallest potential for tax-loss selling (PTS) decile, that
is, stocks with the smallest price decline from the high price, while
losers are stocks in the highest PTS decile, those with the largest
price decline from the high price.
Characteristics of loser stocks are presented in Table 2.2. Loser
stocks fall 74.5 percent from the highest price achieved during the
year. These stocks have a low price and low market capitalization.
For 2000, the median reference price is $1.14, the mean market capi-
Table 2.2. January Effect for Loser Firms
Mean Mean Return
Dec. Jan. Minus Dec.
Median Median 5–Day 5–Day 5–Day
Drop in Price Size Return Return Return
Years Price (%) ($) ($ million) (%) (%) (%)
1988 70.7 0.69 4.28 2.87 6.89 4.02
1989 72.0 0.66 4.74 1.86 6.53 4.67
1990 83.1 0.50 4.35 –1.48 7.15 8.63
1991 71.9 0.69 4.87 4.90 18.27 13.37
1992 72.1 1.25 8.96 2.99 9.74 6.75
1993 65.6 2.00 14.85 3.49 9.21 5.72
1994 74.6 1.50 12.59 –0.49 10.75 11.24
1995 66.3 1.75 13.73 0.52 10.10 9.58
1996 71.7 1.88 18.31 –4.18 13.69 17.87
1997 73.4 1.69 21.35 –3.43 10.66 14.09
1998 81.0 1.50 17.50 3.31 16.11 12.80
1999 72.2 2.94 36.72 5.14 7.95 2.81
2000 93.1 1.14 26.05 –1.04 28.01 29.04
1988–2000 74.5 1.50 13.73 1.11 11.93* 10.82*
The five-day December return is measured from the close of the seventh trading day before
the end of the year to the close of the second trading day before the end of the year. The five-
day January return is for the first five trading days in the following calendar year. If the five-day
December return is for 2000, then the corresponding five-day January return is for 2001.
Statistical significance is at better than 1 percent for returns marked with * and at better than 5
percent for returns marked with +.
The January Effect and the New December Effect 29
talization is $108 million, and the median market capitalization is
$26 million. Next, the returns are reported for five-day periods in
December (excluding the last trading day) and in January.3
day January returns are large throughout 1988–2000 at 11.93 per-
cent. Compared with the five-day December return of 1.11 percent,
the five-day January return is 10.8 percent larger for the loser stocks.
Though not reported here, the volume for loser stocks is about 35
percent smaller in January than in December. For 2000, the volume
is about 45 percent less in January than in December.
Similar to Table 2.2 for loser stocks, Table 2.3 reveals that the win-
ner stocks fall only 1.6 percent from the highest price achieved dur-
ing the year over the 1988–2000 period. In 2000, the average price
drop for winners is only 1.8 percent from the highest price. In gen-
eral, winners are high-priced stocks but not necessarily the largest
stocks by market capitalization. For 2000, the median reference price
is $24.47, the mean market capitalization is $4,125 million, and the
Table 2.3. December Effect for Winner Firms: Turn of Year
Mean Mean Return
Dec. Jan. Minus Dec.
Median Median 5–Day 5–Day 5–Day
Drop in Price Size Return Return Return
Years Price (%) ($) ($ million) (%) (%) (%)
1988 1.2 17.25 71.45 0.46 0.80 0.34
1989 0.5 22.25 175.90 1.57 –0.25 –1.82
1990 3.6 22.75 221.14 –0.12 –3.64 –3.52
1991 0.8 22.44 118.12 4.78 1.44 –3.35
1992 0.6 24.00 167.49 1.43 –0.64 –2.07
1993 1.5 21.50 141.34 0.98 0.20 –0.78
1994 3.4 22.00 147.08 1.13 –0.56 –1.68
1995 0.2 27.50 331.37 1.79 –1.13 –2.91
1996 1.1 22.00 158.21 1.08 0.38 –0.70
1997 0.6 33.00 323.61 1.94 –2.64 –4.59
1998 3.7 31.88 721.05 2.62 0.60 –2.02
1999 2.1 23.91 243.65 3.96 –1.97 –5.93
2000 1.8 24.47 397.95 6.48 –3.66 –10.14
1988–2000 1.6 22.75 175.90 2.16* –0.85 –3.01*
The five-day December return is measured from the close of the seventh trading day before
the end of the year to the close of the second trading day before the end of the year. The five-
day January return is for the first five trading days in the following calendar year. If the five-day
December return is for 2000, then the corresponding five-day January return is for 2001.
Statistical significance is at better than 1 percent for returns marked with * and at better than 5
percent for returns marked with +.
Beyond the Random Walk30
median market capitalization is $398 million. The mean return for
the winner stocks in the five-day December period for 2000 is 6.48
percent. Compared to the gain in December, these stocks lose 3.66
percent in the first five days of the following January (2001). Con-
sistent with the evidence discussed above, the volume for the win-
ner stocks is significantly lower in December than in January, in
accordance with postponement of tax-gain selling to January.
Overall, the absolute return for winner stocks is 3.01 percent
greater for the five-day December period than for the five-day Janu-
ary period. The turnover is more than 40 percent greater for the
five-day period in January than for the five-day period at the end of
A comparison of Tables 2.2 and 2.3 reveals striking differences.
The winner stocks gain in December with significantly lower turn-
over in that month, a phenomenon that is consistent with tax-gain
selling in January. On the other hand, the loser stocks gain in Janu-
ary with a significantly lower turnover, consistent with tax-loss sell-
ing. The results are depicted in Figures 2.3 and 2.4.
A close-up view of the monthly returns for the winner stocks is
presented in Table 2.4. The difference of 0.12 percent per day is ap-
proximately 2.5 percent for the whole month. From Table 2.3, the
five-day December return is 3.01 percent higher than the five-day
January Effect for Loser Firms
Dec. 5-Day Return Jan. 5-Day Return Jan. 5-Day Return Minus
Dec. 5-Day Return
Figure 2.3 The five-day December return and the five-day January return are de-
picted in the figure along with a difference between the two five-day returns for
loser firms over the 1988–2000 period.
The January Effect and the New December Effect 31
December Effect for Winner Firms
Dec. 5-Day Return Jan. 5-Day Return Jan. 5-Day Return Minus
Dec. 5-Day Return
Figure 2.4 The five-day December return and the five-day January return are de-
picted in the figure along with a difference between the two five-day returns for
winner firms over the 1988–2000 period.
Table 2.4. December Effect for Winner Firms: December and January
Mean Mean Minus
Median Median Dec. Jan. Dec.
Price Size Return Return Return
Years ($) ($ million) (%) (%) (%)
1988 17.50 73.77 0.059 0.192 0.141
1989 21.25 130.73 0.075 –0.325 –0.401
1990 20.25 171.43 0.108 0.156 0.048
1991 17.88 66.81 0.216 0.169 –0.047
1992 21.69 194.28 0.156 0.198 0.042
1993 19.50 102.95 0.090 0.153 0.062
1994 20.56 135.43 0.039 0.008 –0.030
1995 27.75 309.34 0.137 0.011 –0.125
1996 29.00 353.26 0.041 0.113 0.075
1997 30.25 330.95 0.233 –0.118 –0.354
1998 30.75 666.30 0.293 0.088 –0.208
1999 22.00 266.55 0.390 –0.054 –0.448
2000 24.88 672.21 0.286 –0.078 –0.368
1988–2000 21.69 194.28 0.163* 0.040 –0.124+
Daily returns in percent. The January return is for the first month in the calendar year follow-
ing the month of December. That is, if the December return is for 2000, then the correspond-
ing January return is for 2001. Statistical significance is at better than 1 percent for returns
marked with * and at better than 5 percent for returns marked with +
Beyond the Random Walk32
return in January, implying that the difference in performance is
concentrated in the ten days around the end of the year. Further, the
volume turnover for winners is significantly higher in January than
The primary explanation for the January effect is that it is related to
tax-loss selling in December: in order to reduce the tax bill, inves-
tors sell losing stocks in December to realize capital losses that are
set off against any realized capital gains. The selling pressure abates
in January, causing the prices of those stocks to rise.
The primary explanation for the December effect is also based on
tax-related selling. If realized capital losses are not available to offset
the capital gains, then those gains are subject to taxation either at the
ordinary income tax rate or at a preferential capital gains tax rate.
Prudent investors postpone realization of capital gains and, conse-
quently, payment of taxes as much as possible. This becomes espe-
cially important and easy at the end of the year, when a delay in the
realization of capital gains can postpone payment of taxes by almost
one year. Thus, it is expected that winner stocks will not be offered for
sale toward the end of the year. Prospective buyers of winner stocks
must bid high to induce shareholders of those stocks to part with their
holdings, thereby causing the observed December effect.
The evidence strongly supports the case for tax-related selling by
investors. First, winners earn higher stock returns in December than
in January, and losers earn less in December than in January (see
Table 2.1). This is further corroborated by the five-day periods sur-
rounding the end of the year in Tables 2.2 and 2.3. Second, if tax-
gain selling causes the abnormal returns for winner stocks, then the
trading volume for those stocks in December should be less than in
And if tax-loss selling causes the abnormal returns for loser
stocks, then the trading volume for those stocks in January should be
less than in December. The evidence is consistent with greater trad-
ing volume for winner stocks in January than in December, and for
greater trading volume for loser stocks in December than in January.
There are other explanations for the January effect, but these have
much weaker support, such as window dressing by institutional
managers, bid-ask bounce, and release of new information. There
are no alternative explanations that are consistent with the Decem-
ber effect. Overall, tax-related selling is the primary candidate for
explaining both the January and December effects.
The January Effect and the New December Effect 33
Why does the January effect persist? Because it is not possible to
arbitrage this anomaly. Note that these stocks are really small: the
January effect occurs only in the bottom 20 percent of all stocks that
trade on organized exchanges and Nasdaq. Thus, out of 6,500 stocks,
the January effect occurs in the bottom 1,300 stocks, which have a
median market capitalization of about $25 million. Investors can-
not buy these stocks in December and sell them in January because
the trading cost is too high, much greater than the potential profit.
There are alternatives to buying and selling stocks that can reduce
trading costs: index futures, options, and mutual funds. However,
none of the alternative financial instruments works for these small-
capitalization stocks, as they are not part of any index, nor do they
have traded options. Mutual funds have low transaction costs com-
pared to stocks or futures. Unfortunately, none of the mutual funds
fits the requirements—either they hold too many stocks or they hold
stocks that are too large. Total market funds, such as Vanguard To-
tal Market, hold about 3,500 of the largest stocks and do not include
any of the smaller stocks. Vanguard Total Market fund’s weighted
market cap is $32.5 billion, much larger than the objective of a $25
million median market cap. Perhaps the best fit is the Dimensional
Fund Advisors U.S. Micro Cap Portfolio (formerly U.S. 9-10 Small
Company portfolio), which claims to invest in the “smallest 4 per-
cent of the market universe.” However, it holds 2,900 stocks that
span the entire bottom 50 percent of the market. As a result, the
average five-day January return over the most recent eleven-year
period is 1.0 percent, compared with 10.8 percent for the January
effect stocks. Though the DFA U.S. Micro Cap portfolio can capture
part of the January effect, the remaining 90 percent of the effect is
untouched. Other small-stock mutual funds have similar composi-
tions, precluding trading strategies to arbitrage the January effect.
Thus, the January effect persists because it can’t be arbitraged away.
Why does the December effect persist? Why hasn’t that been
arbitraged away? Unlike other pricing anomalies, the December
effect is not well known. Investors must know about an anomaly
and be convinced of its existence before they will take action to con-
struct trading strategies. Maybe evidence related to tax-gain selling
is sparse and not yet compelling enough for smart investors to act.
Therefore, the December effect persists. As it becomes better known
the December effect will be arbitraged away and will become less
Beyond the Random Walk34
The December Effect:
The Trading Process and Implementation
As the January effect cannot be arbitraged, the remainder of the
discussion focuses on the December effect alone. There are two al-
ternatives for trading on the December effect: either take a position
at the beginning of December or take a position six trading days
prior to the end of December. Table 2.3 shows that large winner
stocks gain an average of 2.2 percent during the last five trading
days in December, equivalent to about 0.44 percent per day. In this
five-day period during December 2000, as shown in Table 2.3, the
winner stocks gain 6.48 percent (about 1.25 percent per day). From
Table 2.4, the average return for the entire month of December for
large stocks is 0.16 percent per day. In 2000 it is 0.286 percent per
day. Nonetheless, the daily return for the entire month of December
is much less than the daily return for the shorter five-day period.
Therefore, the focus for investors is on trying to capture the five-
day December return, though results for both the full month and
the five-day period are reported.
Since winner stocks are usually of large size, their bid-ask spreads
are low. From Table 2.3, the median stock price is about $24.47. The
bid-ask spread (two transactions) for such stocks is about 0.50 per-
cent. Further, large stocks are unlikely to be affected by large trades
because they tend to be highly liquid. Therefore, it would be rela-
tively easy to identify the winners, buy these stocks at the end of the
seventh trading day prior to year end, and sell them five trading days
later, giving an average return of approximately 1.66 percent (2.16
percent less 0.5 percent for trading costs) over the five-day trading
period, which is in excess of an annualized return of 75 percent.
FUTURES AND EXCHANGE TRADED FUNDS
It is also possible to use other financial instruments that have lower
trading costs to capture the December effect. Because the December
effect stocks are large, the S&P 500 index can possibly provide an
efficient way to trade. The S&P 500 index futures can be traded at a
cost of less than 0.1 percent. Similarly, the exchange-traded S&P 500
index fund (SPDR, AMEX: SPY) has a round-trip transaction cost of
about 0.1 percent. The returns from using S&P500 futures and SPDRs
are given in Tables 2.5 and 2.6, assuming that the total S&P 500 re-
turn is equal to the return on SPDRs. For the period 1988–2001, the
The January Effect and the New December Effect 35
Table 2.5. Trading Strategy for the December Effect: S&P 500 Futures
Futures Futures Futures
Futures Price at Price at Futures Dec.
Price 7th Last 2nd Last Dec. 5–Day
at Day in Day in Return Return
Year Nov. End Dec. Dec. (%) (%)
1988 275.90 281.35 280.40 1.87 -0.34
1989 351.80 347.90 354.95 1.34 2.03
1990 327.20 332.75 331.55 1.16 –0.36
1991 377.60 388.35 416.40 10.75 7.22
1992 432.20 441.95 439.50 1.17 –0.55
1993 463.20 468.90 469.70 0.84 0.17
1994 457.05 464.80 464.40 1.00 –0.09
1995 612.50 612.80 618.20 0.97 0.88
1996 764.90 757.00 758.70 –2.63 0.23
1997 965.80 962.90 979.40 1.28 1.71
1998 1,174.00 1,215.50 1,242.00 6.13 2.18
1999 1,410.80 1,457.00 1,480.00 5.19 1.58
2000 1,341.20 1,279.60 1,353.20 –0.46 5.75
2001 1,141.50 1,142.30 1,159.30 0.68 1.49
The table shows the total returns for the month of December and the last five days of Decem-
ber (excluding the last day) from holding the March S&P 500 index futures contract. All re-
turns are in percent for the entire holding period. Statistical significance at better than 5 percent
for returns marked with +
Table 2.6. Trading Strategy for the December Effect: Mutual Funds and Indexes
S&P S&P 500
Dec. 5–Day Vanguard Dreyfus Scudder Nasdaq
Return Return VFINX DSPIX BTIEX 100 Index
Year (%) (%) (%) (%) (%) (%)
1988 1.85 0.83 0.83 1.16
1989 2.27 2.34 4.08 3.91
1990 2.79 –0.38 –0.12 –1.04
1991 11.43 7.36 7.46 10.45
1992 1.34 –0.26 –0.26 1.21
1993 1.22 0.38 –0.18 0.40 0.30 2.40
1994 1.48 0.41 0.41 0.38 0.47 2.14
1995 1.78 1.37 1.40 1.33 1.35 1.21
1996 –1.98 0.69 0.73 0.73 0.74 –0.91
1997 1.64 1.81 1.86 1.86 1.84 2.34
1998 5.88 2.42 2.40 2.37 2.37 2.44
1999 5.95 2.02 1.98 1.97 1.98 3.41
2000 0.48 5.51 5.52 5.52 5.51 11.51
2001 0.89 1.85 1.88 1.86 1.87 4.09
1993–2001 1.93 1.83 1.78 1.82 1.83 3.18
1988–2001 2.64 1.88 2.00 3.17
The table shows the total returns for last five days of December (excluding the last day) from
holding the S&P 500 mutual funds and the Nasdaq 100 index. All returns are in percent for the
entire holding period.
Beyond the Random Walk36
December return is 2.09 percent using futures and 2.64 percent us-
For the five-day December period, the returns are 1.56
percent and 1.88 percent, respectively. Accounting for the trading
cost of 0.1 percent, the net five-day December return using SPDRs
is at least 1.5 percent during the 1988–2001 period. Clearly, this is a
large return for a short period and does not seem difficult to earn.
Many funds will not charge you a redemption fee provided you don’t
trade multiple times in a year. Since the December effect requires only
one buy and one sell in a year, it is unlikely that there will be any fees.
Large, no-load S&P 500 index funds that are open to retail investors
include Vanguard’s 500 Index Fund (VFINX), Dreyfus’s index fund
(DSPIX), and Scudder Equity 500 Index Investment Fund (BTIEX).
The fund returns are reported in Table 2.6. The returns earned are
almost identical to those earned by the S&P 500. However, since the
transaction cost is close to zero, the net return is about 1.8 percent
over a five-day period. Therefore, index mutual funds are a superior
vehicle for capturing the December effect.
In addition to the S&P 500, the Nasdaq 100 represents a group of
large stocks. Since the Nasdaq 100 is constructed solely on the basis
of market capitalization and consists of only 100 stocks, instead of
500 as in the S&P 500, it is likely to reflect a greater concentration of
large stocks. However, on the downside, the Nasdaq 100 is signifi-
cantly riskier and more volatile than the S&P 500. The five-day
returns for the Nasdaq 100 index are reported in Table 2.6. It can
be seen that the Nasdaq 100 generates a whopping return of 3.18
percent (and 3.08 percent after transaction costs) over the five-day
period in December compared with a 1.56 percent return for the
TRADING STRATEGY AND RESULTS
To capitalize on the December effect, this trading strategy would be
1. Buy SPDR, go long in S&P 500 index futures, buy an index
mutual fund, or buy the Nasdaq 100 toward the close of trad-
ing on the seventh last trading day in December.
2. Close the position toward the close of trading on the second
last trading day in December. Buying on the seventh last trad-
The January Effect and the New December Effect 37
ing day and selling on the second last trading gives the five-
day return for capturing the December effect.
As shown in Tables 2.5 and 2.6, the five-day return in December
is between 1.56 percent and 3.08 percent after transaction costs, de-
pending on the type of instrument employed to capture the Decem-
The December Effect:
The evidence presented in this chapter and the trading strategy rec-
ommendations are based on past data. Since future market condi-
tions and market patterns may be completely different, there is no
certainty that the December effect will continue or be profitable in
Only the raw returns from capturing the December effect have
been reported in the analysis. In addition, the risk of trading the
December effect has not been considered in evaluating the return. If
the risk in the last few days of December is significantly higher than
usual, the attractiveness of the December effect will decline.
The January Effect:
What Can Investors Do?
Though arbitraging a significant part of the January effect is not
possible, investors can utilize this knowledge to change their own
trading patterns. Instead of selling losers in December, they should
wait until January. The cost of paying taxes a year earlier is much
less than the expected appreciation of the stock they hold. This can
be illustrated easily: Assuming an average capital loss of 65 percent
and the new tax rate of 15 percent, the realizable tax benefit is 10
percent. Postponement of realization of this tax benefit by one year
will cost the investor one percent at a 10 percent interest rate. The
January effect of about 10 percent easily exceeds this loss due to post-
ponement. Similarly, investors should advance their purchases, if any,
of small-cap stocks from January to December. A change in the trad-
ing patterns can help investors from not being hurt by the January
effect even if they can’t directly use it to earn arbitrage profits.
Beyond the Random Walk38
• Investors may choose not to sell their winners in December in
order to postpone payment of taxes. By waiting a few days,
they can postpone payment of taxes by almost a year. Since the
supply of winner stocks will be restricted in December or in
the last few days of December, winner stocks are likely to ap-
• Evidence shows that winner stocks earn about 2.16 percent in
the last five days of December.
• As the winner stocks are generally large stocks, the December
effect can be easily captured using instruments that track the
S&P 500 index, such as spiders, index futures, and index funds,
or those that track the Nasdaq 100. The five-day return is 1.56
percent for S&P 500–related instruments and 3.08 percent for
the Nasdaq 100 index.
• While the January effect cannot be arbitraged easily, investors
can alter their trading patterns so that they are not hurt by the
January effect. In particular, investors should buy loser stocks
in December instead of January, and they should sell loser
stocks in January instead of December.
The December effect refers to appreciation of winner stocks in the
last few days of the year. This effect has been persistent over the last
decade, even in 2000 and 2001, when not many stocks appreciated.
The December effect of 1.5 percent could have been profitably ex-
ploited during that period using a simple technique: hold the S&P
500 index for about a week at the end of the year.
http://www.cme.com: The Chicago Mercantile Exchange is the primary
exchange for trading stock index futures.
http://www.indexfunds.com: Provides a list of mutual funds and exchange-
traded funds indexed to the S&P 500 and the Nasdaq 100.
http://www.vanguard.com: Sites of mutual fund families that offer index
funds. The first two do not impose any penalty for frequent trading.
The January Effect and the New December Effect 39
References for Further Reading
Agrawal, Anup, and Kishore Tandon. 1994. Anomalies or Illusions? Evidence from
Stock Markets in Eighteen Countries. Journal of International Money and Finance
Barry, Christopher B., and Stephen J. Brown. 1984. Differential Information and
the Small Firm Effect. Journal of Financial Economics 13(2), 283–94.
Bhabra, Harjeet S., Upinder S. Dhillon, and Gabriel G. Ramírez. 1999. A Novem-
ber Effect? Revisiting the Tax-Loss-Selling Hypothesis. Financial Management
Bhardwaj, Ravinder, and Leroy Brooks. 1992. The January Anomaly: Effects of
Low Share Price, Transactions Costs, and Bid-Ask Bias. Journal of Finance 47,
Chen, Honghui, and Vijay Singal. 2003a. The January Effect: A Re-Examination.
Working paper, Department of Finance, Virginia Tech.
——— . 2003b. A December Effect with Tax-Gain Selling? Financial Analyst Jour-
Constantinides, George M. 1984. Optimal Stock Trading with Personal Taxes:
Implications for Prices and the Abnormal January Returns. Journal of Financial
Economics 13(1), 65–89.
Haugen, Robert A., and Philippe Jorion. 1996. The January Effect: Still There Af-
ter All These Years. Financial Analyst Journal 52(1), 27–31.
Haugen, Robert A., and Josef Lakonishok. 1988. The Incredible January Effect: The
Stock Market’s Unsolved Mystery (Homewood, Ill.: Dow Jones–Irwin).
Keim, Donald B. 1983. Size-Related Anomalies and Stock Return Seasonality: Fur-
ther Empirical Evidence. Journal of Financial Economics 12, 13–32.
Lakonishok, Josef, Andrei Shleifer, Richard Thaler, and Robert Vishny. 1991. Win-
dow Dressing by Pension Fund Managers. American Economic Review 81, 227–31.
Poterba, James M., and Scott J. Weisbenner. 2001. Capital Gains Tax Rules, Tax-Loss
Trading, and the Turn-of-the-Year Returns. Journal of Finance 56(1), 353–68.
Reinganum, Mark. 1983. The Anomalous Stock Market Behavior of Small Firms
in January: Empirical Tests for Tax-Loss Selling Effects. Journal of Financial Eco-
nomics 12, 89–104.
Wachtel, Sidney. 1942. Certain Observations on Seasonal Movement in Stock Prices.
Journal of Business (April), 184–93.
1. This chapter is based on research in Chen and Singal (2003a, 2003b). Other
works used in this chapter include Bhabra, Dhillon, and Ramírez (1999),
Constantinides (1984), Keim (1983), Poterba and. Weisbenner (2001), and
Haugen and Jorion (1996).
2. For example, see the Wall Street Journal, December 6, 2001.
3. Excluding the last day of the year is common in many studies because of low
trading volume on that day.
4. The abnormal return is calculated as the actual return minus the expected
return. Expected return is the risk-free rate plus market risk premium times
the beta of the stock.
5. The difference in the return to SPDRs and futures may be attributable to dif-
ferences in closing times.
Beyond the Random Walk40
The weekend effect refers to relatively large returns on Fridays com-
pared to those on Mondays. Whereas the Friday returns exceed 0.20%,
the Monday returns are close to zero or negative resulting in a weekend
effect for an equally weighted index of 0.34 percent. On the other hand,
the weekend effect for a value-weighted index has fallen to zero during
Short sellers may be responsible for the weekend effect because they
do not want to keep speculative positions open around the weekend.
Accordingly, they close the short positions by buying back on Fridays
and reopen them by short selling on Mondays causing higher returns on
Fridays and lower returns on Mondays.
It is, however, not easy to capture the weekend effect with current
financial instruments because the trading costs can be large. Nonethe-
less, investors should recognize the weekend effect and avoid buying
on Fridays and selling on Mondays. Instead, they should buy stocks on
Mondays and sell on Fridays.
The weekend effect is best defined as a Friday’s return minus the fol-
lowing Monday’s return for a single security or a portfolio of secu-
This definition captures the preweekend positive returns
(higher returns on Fridays) and the postweekend negative returns
(lower returns on Mondays). In the absence of seasonality in re-
turns, firms should, on average, earn the same return on all days of
the week, especially on adjacent trading days. Thus, the weekend
effect should be zero for all securities and should be unaffected by
The Weekend Effect
The Weekend Effect 41
the risk or volatility of a security or by trends in returns.2
discussion that follows, the last trading day of the week is called
Friday, whether it is actually a Thursday or a Friday. Similarly, the
first trading day of the week is called Monday, whether it is a Mon-
day or a Tuesday.
Beginning with the discovery of the weekend effect by Ken French
at the University of Chicago in 1980, there is much evidence in sup-
port of higher returns on Fridays and lower returns on Mondays.
Numerous academic and practitioner papers have examined the
existence and causes of the weekend effect and discovered many
stylized facts, such as the weekend effect has been in existence for
more than a hundred years, Friday returns are lower when there is
Saturday trading, the weekend effect is larger around long week-
ends, a larger number of stocks rise before a holiday than after the
holiday, and the weekend effect has been weakening over the past
decade. Even a book based on the weekend effect was published in
1986: Yale Hirsch’s Don’t Sell Stocks on Monday. A detailed discus-
sion of the weekend effect follows.
An examination of daily returns for all common stocks traded on
the NYSE, AMEX, and Nasdaq is instructive. The returns are pre-
sented in Table 3.1 for the period July 1962–December 2001. Two
types of returns are reported: an equally weighted return (the mean
return to all stocks with all stocks carrying equal weights) and a
value-weighted index (the mean return to all stocks where each
stock’s weight is equal to its market capitalization). The first two
rows have the returns for the entire period, while the remaining
rows have returns by decades. The table shows that Monday re-
turns are significantly negative, whereas Wednesday and Friday
returns are significantly positive for both the equally weighted and
the value-weighted indexes. For the equally weighted index, the
Friday return is much larger than the return on any other day of the
week, and the Monday return is the smallest. For the value-weighted
index, the Friday and Wednesday returns are comparable, but the
Monday return is again the smallest (most negative). It is no won-
der that the weekend effect, which is the difference between the
Friday return and the Monday return, is positive and significant.
Overall, the weekend effect for an equally weighted index is 0.339
percent. This translates into an annual return of about 17 percent.
For a value-weighted index, the return is 0.15 percent, or about 8
Beyond the Random Walk42
percent per year. The value-weighted index is tilted heavily toward
stocks with high market capitalization, such as General Electric and
Table 3.1 also depicts the time trend in the weekend effect. It can
be observed that the weekend effect based on the equally weighted
index is almost invariant with time. The weekend effect was 0.326
percent per weekend during the 1960s, 0.327 percent during the
1970s, 0.403 percent during the 1980s, and 0.304 percent during the
1990s. It is statistically significant in all four subperiods. In the last
period, the Monday return is close to zero, but the Friday return is
essentially unaltered. The story with the value-weighted index is
Table 3.1 The Weekend Effect
July 1962 to 2001: Daily Returns (in percent)
Mon. Tue. Wed. Thu. Fri. (Fri.–Mon.)
Overall for July 1962 to 2001
EW –0.093* 0.000 0.133* 0.125* 0.246* 0.339*
EW –0.105* –0.008 0.176* 0.074+
VW –0.124* 0.022 0.145* 0.028 0.131* 0.255*
–0.019 0.112* 0.115* 0.245* 0.327*
0.035 0.098* 0.049 0.111* 0.211*
EW –0.173* –0.038 0.108* 0.123* 0.231* 0.403*
VW –0.078 0.062 0.112* 0.049 0.109* 0.187*
EW –0.021 0.056 0.144* 0.174* 0.283* 0.304*
VW 0.063 0.053 0.057 0.057 0.050 –0.013
The sample consists of all ordinary common shares traded on NYSE, AMEX, or Nasdaq. Mon-
day refers to the first trading day of the week, while Friday refers to the last trading day of the
week. The weekend effect refers to the difference between a Friday’s return and the following
Monday’s return. The equally weighted index returns of all stocks are given in the rows titled
“EW,” while value-weighted index returns are in the rows titled “VW.” Statistical significance
is at better than 1 percent for returns marked with * and at better than 5 percent for returns
marked with +
The Weekend Effect 43
different. The difference among day-by-day returns becomes less
and less important with time until it completely disappears in the
1991–2001 period. For the last decade, the value-weighted daily re-
turn is between 0.05 percent and 0.063 percent irrespective of the
day of the week, which means that there is no weekend effect. In-
deed, the last column shows that the weekend effect based on the
value-weighted index falls gradually from 0.255 percent in the 1960s
to 0.211 percent in the 1970s to 0.187 percent in the 1980s and to an
insignificant –0.013 percent in the 1990s. It is important to note that
the persistence of the weekend effect for the equally weighted in-
dex is broad-based and not due to one or two abnormal years. (As
explained in subsequent sections, the weekend effect is due to short
sellers, who migrate to the options market once options become avail-
able. Since options are more easily available and less expensive for
large stocks, the weekend effect for the value-weighted index begins
to disappear in later years. For an average stock, however, options
are either unavailable or too expensive to trade, causing the weekend
effect for the equally weighted index to be relatively unchanged.)
Mon. Tue. Wed. Thu. Fri. (Fri.– Mon.)
Figure 3.1 The first five columns show the weekday returns for an equally weighted
index over the 1962–2001 period. The last column shows the weekend effect, which
is the difference between the Friday return and the Monday return.
Beyond the Random Walk44
Short Selling as
the Primary Explanation
Given evidence of the weekend effect, what is the cause? The pri-
mary explanation for the weekend effect relies on the behavior of
short sellers with regard to unhedged short sales, as distinct from
hedged short sales.3
Hedged short sales include merger arbitrage
where an investor short-sells the bidder and buys the target (see
Chapter 9), index arbitrage between futures and cash markets, short
selling by put option writers to hedge their positions, shorting
against the box (short-selling a stock that is held long in another
account) to postpone realization of capital gains, and other similar
activities where the short position is hedged by an offsetting simi-
lar position. On the other hand, unhedged or purely speculative
short sales are naked positions based on the expectation (or hope)
that the price of the shorted security will fall.
Hedged short sales are not very risky because an equivalent trade
hedges the movement in the short-sold security. But speculative
short positions are not hedged and require close monitoring. Un-
like a long position, where the loss is limited to the value of the
holding, the downside risk of a speculative short position is theo-
retically unlimited. A large price move can wipe out the owner’s
equity in an account. For that reason, “[p]ros warn that speculative
short-selling, in which an investor simply sells a stock short hoping
the price will fall, is one of the riskiest strategies going. . . . [I]t is not
something a part-time investor should engage in” (Smith 1999).
While close monitoring during trading hours can limit the po-
tential loss of a short seller, nontrading hours introduce special risk
as the short sellers are unable to trade. The inability to trade implies
that short sellers are unable to control losses that may occur due to
news or stock price moves after market hours. Thus, short sellers
are averse to holding positions over nonmarket hours and like to
close positions at the end of the day and reopen them the next morn-
ing. However, the transaction costs of closing and opening a posi-
tion, the uptick rule, and limited availability of shares to short-sell
make it expensive for the short sellers to trade too often.4
end becomes a natural break point, as it is a long period (65.5 hours
for a regular weekend and 89.5 hours for a long weekend) of non-
trading compared to the normal interday period (17.5 hours) of non-
Thus, the inability to trade over the weekend makes many
short sellers close their speculative positions at the end of the week
and reopen them at the beginning of the following week, leading to
The Weekend Effect 45
the weekend effect. The stock prices rise on Fridays as short sellers
cover their positions, and fall on Mondays as short sellers reestab-
lish new short positions.
EVIDENCE IN SUPPORT OF SHORT SELLING
If short selling is responsible for the weekend effect, then stocks
with a higher level of short sales should have a stronger weekend
effect. That is indeed the case. To relate the weekend effect to short
sales, all stocks are divided into ten size deciles (ten equal groups
based on market capitalization). Each size decile is then subdivided
into four quartiles (four groups of equal size) based on relative short
interest (RSI), where RSI is measured as the short interest divided
by the number of shares outstanding. Stocks in the highest RSI
quartile within a size decile have a weekend effect that is more than
40 percent greater than stocks in the lowest RSI quartile for the same
size decile: the weekend effect increases from 0.27 percent for the
lowest quartile to 0.39 percent for the highest quartile.
The weekend effect should depend on speculative short interest,
not total short interest. However, the test discussed in the previous
paragraph does not distinguish between speculative short interest
and hedged short interest. Initial public offerings (IPOs) are ideal
for testing the effect of speculative short sales on the weekend re-
turns, because they are likely to have only speculative short posi-
tions. IPOs are not good candidates for hedged short sale activity
because (1) they are usually not part of an index (no index arbi-
trage), (2) they are not likely to be takeover candidates (no merger
arbitrage); and (3) the high volatility of IPOs inhibits other types of
nonspeculative short sellers from trading them. Results with IPOs
show that the weekend effect increases from 0.12 percent for the
low RSI quartile to 0.59 percent for the high RSI quartile. The week-
end effect is nearly four times greater for IPOs in the top 25 percent
by RSI than for IPOs in the bottom 25 percent by RSI.
If speculative short sales are so risky that short sellers must re-
sort to trading around the weekend, isn’t there another way of trad-
ing on negative information? Unfortunately, there was no alternative
until put options were introduced in 1977. Put options are consid-
ered a substitute for short selling, as they allow the buyer to gain
from a fall in price. Put options are more expensive because of the
option premium but entail lower risk. Speculative short sellers tend
to prefer put options because of the high risk associated with specu-
lative short positions, and would migrate to the options market if
options are available. The consequent reduction in speculative short
Beyond the Random Walk46
interest would then coincide with a reduction in the weekend ef-
fect. However, as traders are very concerned with the cost of trad-
ing, the migration to the options market will occur only for stocks
with actively traded options. Otherwise, the high cost of trading in
illiquid options markets makes it uneconomical to migrate.
Further evidence of the importance of short selling as an expla-
nation for the weekend effect becomes apparent when a test is con-
ducted to compare the weekend effect for the one hundred most
actively traded stocks (by stock volume) with those of the one hun-
dred least actively traded stocks. The test shows that the weekend
effect weakens significantly after 1977 and disappears in the 1990s
for the most actively traded stocks. On the other hand, the weekend
effect continues unabated for the least actively traded stocks through
the 1980s and 1990s. These results are reinforced by regression re-
sults that suggest that stocks with higher put option activity have a
lower weekend effect, a finding that is consistent with the substitu-
tion agreement suggested in the preceding paragraph.
The evidence presented above supports the role of speculative
short sellers in contributing to the weekend effect. Some other ob-
served facts related to the weekend effect are also consistent with
the short-selling explanation:
• The weekend effect has been in existence for more than a hun-
dred years: Short selling has been permitted on U.S. exchanges
since 1858. After the stock market crash in 1929, there was an
attempt to curb the practice. However, short selling was actu-
ally disallowed on only two days in 1931. New rules govern-
ing short selling were introduced by the SEC under the
Securities and Exchange Act of 1934.
• Friday returns are lower when there is Saturday trading: Con-
sistent with the short selling explanation, short sellers may wait
until Saturday to close their positions, reducing the Friday re-
• The weekend effect is larger around long weekends: When the
market is closed for a holiday weekend, more short sellers are
likely to close short positions by buying back on the last trad-
ing day of the week and reopen their positions after the mar-
ket reopens. This will result in a larger weekend effect.
• A larger number of stocks rise before a holiday than after a
holiday: Short sellers trade around holidays in the same man-
ner as they do around weekends, giving rise to the returns
documented around holidays.
The Weekend Effect 47
• The weekend effect is more pronounced for stocks held by in-
stitutions: Since individuals tend not to engage in short sell-
ing, the weekend effect will be greater where institutional
investors are more active.
• The weekend effect has become weaker for the most actively
traded stocks during the 1990s: As explained above, the mi-
gration of short sellers to the options market will result in the
disappearance of the weekend effect for the more actively
traded stocks, which are usually firms with a large market capi-
Many potential explanations have been proposed and investigated:
measurement errors, specialist-related biases in prices, timing of
corporate releases after Friday’s close, reduced institutional trad-
ing and greater individual trading on Mondays, and Daylight Sav-
ing Time changes for two weekends a year. These explanations
account for some portion of the weekend effect. For example, the
announcement of earnings and dividends on Friday after the close,
especially if the news is negative, can explain a small proportion
(3.4 percent) of the weekend effect. Further, the tendency to post-
pone release of this news is not restricted to firms in any particular
size decile. This delay in settlement of trades can explain about 17
percent of the weekend effect.
Another possible explanation relates to the bid-ask bounce. If
stocks trade at the ask price on Fridays at market close and at the
bid price on Mondays, it will seem that the Monday return is nega-
tive even when no change in price has taken place. For example,
consider a stock that has a bid of $5.00 and an ask of $5.05. Assume
that the price is unchanged on Friday and the following Monday.
However, if the closing trade occurs at the ask price of $5.05 on
Friday but the closing trade occurs at the bid price of $5.00 on Mon-
day, the computed return for Monday will be –1 percent. This ex-
planation implies that there is really no weekend effect—that the
bid-ask bounce is misinterpreted as a weekend effect. However, es-
timates indicate that the bid-ask bounce can account for 32 percent
of the observed weekend effect, but only for small stocks. For large
stocks, the bid-ask bounce can explain less than 10 percent of the
From the above, it can be seen that all of the alternative explana-
tions account for only a small portion of the weekend effect. Though
Beyond the Random Walk48
short selling may not be the only explanation, it can explain at least
30 percent and up to 80 percent of the weekend effect. Therefore,
trading strategies constructed here are based on the assumption that
speculative short selling is the primary explanation.
Since existence of the weekend effect has been known for more than
twenty years, why hasn’t it been arbitraged away? There are two
possible reasons. First, the cause of the weekend effect was unknown
until the discovery of the short-selling explanation in a paper pub-
lished in 2003. An anomaly without a reasonable explanation is very
risky for an arbitrageur because the mispricing can unpredictably
cease to exist; in fact, the weekend effect has disappeared for actively
traded stocks. Further, if the arbitrageur does not know the reason, it
is not possible to refine the trading strategy for capturing the highest
return. This leads to the second reason for persistence: the weekend
effect is not large. For an equally weighted index, the weekend effect
was about 0.3 percent during 1990–2001. For a value-weighted in-
dex, the weekend effect does not exist.As the equally weighted index
consists of small stocks, the trading costs may be larger than the week-
end effect unless the investor can narrow the list of stocks to a few
that can be selectively traded.
The Trading Process
This section attempts to construct a trading strategy in which the
costs of trading are smaller than the weekend effect.
The evidence relating to the weekend effect reveals many deter-
minants. These factors will help in identifying stocks that exhibit
the greatest weekend effect. Since it is not possible to distinguish
between speculative and nonspeculative short interest, only those
firms that are not good candidates for hedged short sales will be
• The stock should have a high level of relative short interest. A
minimum RSI of 5 percent is appropriate.
• The stock should not have actively traded options. The maxi-
mum average daily option volume should be one thousand
contracts (one hundred thousand shares). Fewer than five hun-
dred stocks have actively traded options.
The Weekend Effect 49
• The stock should not be engaged in any significant corporate
events such as mergers, equity issues, and so on, because these
events may result in hedged short selling.
• The stock should not be part of the S&P 500 index or the Nasdaq
100 index. These stocks are subject to significant hedged short-
• To minimize the transaction costs, the stock price must be at
least $10 and the daily stock volume should exceed one hun-
dred thousand shares.
• Stocks trading on Nasdaq are better suited to the weekend ef-
fect than NYSE stocks because Nasdaq stocks are smaller in size
and are of greater interest to short sellers due to their volatility.
It is anticipated that a carefully selected set of stocks may generate a
weekend effect of about 0.50 percent. In addition to capturing the
weekend effect by trading individual stocks, investors could alter
their trading behavior at little or no extra cost. In particular, stocks
not in the top five hundred stocks by volume should be bought on
Mondays and sold on Fridays rather than on other days of the week.
As mentioned in the summary at the start of this chapter, it is not
possible to generate large tradable profits from the weekend effect
based on financial instruments available at the present time. None-
theless, this section shows the construction of a trading strategy and
the results using a variety of different instruments.
The criteria for selection of stocks outlined in the previous sec-
tion imply that selected stocks should not be large because they
will have actively traded options for which the weekend effect has
disappeared. At the same time, the stocks should be somewhat liq-
uid so that the trading costs are low. Short sellers will not trade
illiquid stocks. For example, firms in the bottom 10 percent by size
have close to zero short interest. Only the top 50 percent, by size,
have a significant level of short interest (more than 1 percent of shares
outstanding). The Russell 2000 index, while not perfect, comes clos-
est to capturing the stocks with the highest weekend effect. The in-
dex excludes stocks that fall in the bottom half of the market and
also excludes large stocks (the top one thousand) that are likely have
actively traded options. However, the Russell 2000 contains many
stocks with insufficient volume or with a very low stock price.
Beyond the Random Walk50
Returns for the Russell 2000 are presented in Table 3.2 for the
1992–2001 period in two-year intervals. In addition, returns for the
Russell 1000 (the large-cap stocks) and the equally weighted index
and the value-weighted index are given for comparison. It can be
seen that the weekend effect for the equally weighted index is posi-
tive and significant throughout the entire period, with an average
of 0.3 percent. On the other hand, the weekend effect for the value-
weighted index is never positive and significant. The overall mean
weekend effect for the value-weighted index is an insignificant –0.01
percent. The Russell 2000 has a positive weekend effect that is sig-
nificant for the overall ten-year period, with a mean of 0.17 percent.
However, it is not significant for any of the biennial periods except
1994–95. Thus, the Russell 2000 index fares much worse than the
equally weighted index in Table 3.1. However, the Russell 2000 is
our best bet for capturing the weekend effect, as the equally weighted
index is not available in a tradable form.
Four financial instruments related to the Russell 2000 and indi-
vidual stocks as vehicles for capturing the weekend effect are de-
Table 3.2 Weekend Effect During 1992–2001 (in percent)
Russell Weighted Russell Weighted
2000 Index 1000 Index
Weekend Weekend Weekend Weekend
Year Effect Effect Effect Effect
1992–1993 mean 0.126 0.253* –0.189+
1992–1993 median 0.027 0.232* –0.134+
1994–1995 mean 0.137+
0.291* –0.017 0.013
1994–1995 median 0.106 0.296* 0.054 0.048
1996–1997 mean 0.017 0.176+
1996–1997 median 0.027 0.137* –0.027 –0.025
1998–1999 mean 0.179 0.365* 0.128 0.117
1998–1999 median 0.107 0.295* 0.303 0.213
2000–2001 mean 0.352 0.292+
2000–2001 median 0.142 0.208+
Overall mean 0.167* 0.304* –0.057 –0.013
Overall median 0.070+
0.232* 0.000 –0.000
The weekend effect refers to the difference between a Friday’s return and the following Monday’s
return. Statistical significance is at better than 1 percent for returns marked with * and at better
than 5 percent for returns marked with +
The Weekend Effect 51
EXCHANGE TRADED FUNDS
The first financial instrument for the Russell 2000 is an exchange-
traded fund, iShares Russell 2000 (AMEX: IWM). The fund has a
daily volume in excess of 1.5 million shares. However, the bid-ask
spread is approximately 0.10 percent, which implies that one round
trip to capture the weekend effect will cost 0.10 percent.As the week-
end effect associated with the Russell 2000 is estimated at 0.17 per-
cent, the transactions costs will reduce the total return to an
unexciting 0.07 percent.
Mutual funds are another possible vehicle for capturing the week-
end effect. There are many mutual funds that track the Russell 2000,
including Vanguard’s Small Cap Index, E*trade Russell 2000 Index,
Federated Mini-Cap Index, and Merrill Lynch Small Cap, to name a
few. However, the typical mutual fund company does not allow
one trade per weekend or fifty trades a year. Fortunately, two mu-
tual fund companies, Rydex and ProFunds, offer funds without re-
strictions on the frequency of trading. Rydex has one fund that tracks
the Russell 2000, while ProFunds has three funds related to the
Russell 2000, including one that is the inverse of Russell 2000. Un-
fortunately, the funds do not have a long enough history for any
reliable conclusions. The Rydex Mekros Fund was first offered in
November 2000, the ProFund Small Cap in September 2001, the
ProFund UltraSmall-Cap in February 2000, and the ProFund Short
Small-Cap in May 2002. At least five years of historical data should
be available to evaluate the performance of a fund with reference to
Russell 2000 futures contracts provide one more avenue for trad-
ing. Unfortunately, the trading in Russell 2000 futures is quite lim-
ited, averaging between two thousand and five thousand contracts
per day. Thus, the round-trip trading cost of 0.1 to 0.2 percent deci-
mates the expected returns from the weekend effect. If trading in
Russell futures becomes more active, then it might become possible
to use futures contracts to capitalize on the weekend effect.
In addition to options on individual stocks, options are available on
popular indexes, including the Russell 2000. Unfortunately, as with
Beyond the Random Walk52
futures, the Russell 2000 index options are very thinly traded, with
a daily volume of fewer than one hundred contracts. Consequently,
the bid-ask spread and the premium costs are too high for Russell
2000 index options relative to the weekend effect.
Stocks that meet the previously outlined conditions can be selected
for trading. Begin with the short interest position of stocks made
public by various stock exchanges in the third week of each month.
The information containing the short interest positions also reports
the average daily volume for the previous month. Since both short
interest and volume are given, it is easier to calculate the short in-
terest ratio (short interest divided by volume) than the relative short
interest (short interest divided by number of shares outstanding).
Therefore, the short interest ratio is used for the remaining analysis.
The month of analysis is December 1999. All stocks with a short
interest ratio of at least five days and a daily average volume of at
least one hundred thousand shares are selected. Instead of check-
ing the option activity and index membership, both of which are
time-consuming to verify, a market capitalization limit can be im-
posed. Since the largest company in the Russell 2000 has a market
capitalization of a little in excess of $1 billion, the market capitaliza-
tion of the selected companies must be at most $1 billion and the
stock price must be at least $10. Sixty-five Nasdaq firms meet these
For the year 2000, the weekend effect for the sixty-five Nasdaq
firms has a mean of 0.50 percent and a median of 0.62 percent.
Though both of these are larger than the weekend effect for the
equally weighted index, the bid-ask spread for these stocks is even
larger, at 0.80 percent. Because the trading costs exceed the week-
end effect, stocks cannot be used for capturing the weekend effect.
The evidence presented in this chapter is based on past data. Since
future market conditions and market patterns may be completely
different, there is no certainty that the past weekend price patterns
will continue in the future.
The Weekend Effect 53
• The weekend effect, defined as the Friday return minus the
subsequent Monday’s return, should be zero.
• Evidence reveals that the weekend effect is about 0.34 percent
for an equally weighted index and 0.15 percent for a value-
weighted index. In general, the Monday return is negative and
the Friday return is positive. Evidence also reveals that the
weekend effect has weakened for actively traded stocks dur-
ing the 1990s.
• It seems that speculative short sellers are largely responsible
for the weekend effect. Since short positions are very risky, short
sellers do not want to hold them over the weekend. Therefore,
some of them close their positions on Fridays and reopen them
on Mondays, causing the weekend effect. When options are
available and actively traded, the short sellers migrate to the
options market. This move makes the weekend effect disap-
pear among large stocks with actively traded options. Alterna-
tive explanations of the weekend effect cannot explain a
significant part of the weekend effect.
• Due to the small absolute magnitude of the weekend effect, it
is not possible to arbitrage the weekend effect. New instru-
ments with lower trading costs may present an opportunity to
arbitrage in the future.
• In any case, investors must recognize the existence of the week-
end effect. Accordingly, whenever it is possible to alter the tim-
ing of trades, investors should sell on Fridays and buy on
There is strong evidence regarding the weekend effect for stocks with
a high level of short interest but without actively traded options. Typi-
cally, these are stocks that are not among the top five hundred stocks
by market capitalization. The weekend effect for an equally weighted
index is about 0.34 percent. No efficient trading strategies exist to
arbitrage the weekend effect due to relatively high trading costs.
However, investors can still profit from the weekend effect by
slightly altering their trading behavior. That is, investors should sell
stocks on Fridays and buy them on Mondays.
Beyond the Random Walk54
Short Interest Data
http://www.nyse.com. Go to “Press Room,” then to “Press Releases” and pick
“Short Interest” from “Sort by Category.” Scroll down to the bottom of the
news item to get the latest table of short interest positions. Data are available
for sale from www.nysedata.com.
http://www.marketdata.nasdaq.com/mr4c.html: Has historical short interest
data for Nasdaq issues back to 1995.
http://www.amextrader.com/asp/short_interest.asp: Has historical short
interest data for AMEX issues back to 1995.
Activity in Options Markets
http://www.cboe.com/MktData/AvgDailyVol.asp: Has options volume data
for the Chicago Board Options Exchange, which accounts for roughly one-
half the total options volume.
http://www.optionsclearing.com: Site of Options Clearing Corporation, which
is responsible for all U.S. options exchanges.
Constituents of Equity Indexes
http://www.standardandpoors.com: Has a list of constituents of the S&P 500.
You can choose either an Excel or .csv format.
http://www.nasdaq.com has a list of constituents of the Nasdaq 100.
Russell 1000, Russell 2000, and Russell 3000.
References for Further Reading
Ariel, Robert. 1990. High Stock Returns Before Holidays: Existence and Evidence
on Possible Causes. Journal of Finance 45, 1611–26.
Chan, Su Han, Wai-Kin Leung, and Ko Wang. 2003. The Impact of Institutional
Investors on the Monday Seasonal. Journal of Business, forthcoming.
Chen, Honghui, and Vijay Singal. 2003. Role of Speculative Short Sales in Price
Formation: Case of the Weekend Effect. Journal of Finance 58, 685–705.
Damodaran, Aswath. 1989. The Weekend Effect in Information Releases: A Study
of Earnings and Dividend Announcements. Review of Financial Studies 2, 607–23.
Dyl, Edward A., and Stanley A. Martin Jr. 1985. Weekend Effects on Stock Re-
turns: A Comment. Journal of Finance 40, 347–50.
Fosback, Norman G. 1986. Stock Market Logic. Institute for Economic Research, FL.
French, Kenneth R. 1980. Stock Returns and the Weekend Effect. Journal of Finan-
cial Economics 8, 55–69.
Gibbons, Michael R., and Patrick Hess. 1981. Day of the Week Effects and Asset
Returns. Journal of Business 54, 579–96.
Hirsch, Yale. 1986. Don’t Sell Stocks on Monday (New York: Facts on File).
Jaffe, Jeffrey, and Randolph Westerfield. 1985. The Week-End Effect in Common
Stock Returns: The International Evidence. Journal of Finance 40(2), 433–54.
Kamstra, Mark J., Lisa A. Kramer, and Maurice D. Levi. 2000. Losing Sleep at the
Market: The Daylight Saving Anomaly. American Economic Review 90, 1005–11.
The Weekend Effect 55
Keim, Donald B., and Robert F. Stambaugh. 1984. A Further Investigation of the
Weekend Effect in Stock Returns. Journal of Finance 39, 819–35.
Lakonishok, Josef, and Maurice Levi. 1982. Weekend Effects on Stock Returns: A
Note. Journal of Finance 37, 883–89.
Lakonishok, Josef, and Seymour Smidt. 1988. Are Seasonal Anomalies Real? A
Ninety-Year Perspective. Review of Financial Studies 1, 403–25.
Rogalski, Richard J. 1984. New Findings Regarding Day-of-the-Week Returns over
Trading and Non-Trading Periods: A Note. Journal of Finance 39, 1603–14.
Sias, Richard, and Laura Starks. 1995. Day-of-the-Week Anomaly: The Role of
Institutional Investors. Financial Analyst Journal 51(3), 57–66.
Smith, Geoffrey. 1999. “You, Too, Can Short Stocks.” Business Week, March 22.
Wang, Ko, Yuming Li, and John Erickson. 1997. A New Look at the Monday Ef-
fect. Journal of Finance 52, 2171–86.
1. This chapter draws extensively from the author’s prior work, in particular
from Chen and Singal (2003). Other work used in this chapter includes French
(1980), Gibbons and Hess (1981), Lakonishok and Smidt (1988), Keim and
Stambaugh (1984), Jaffe and Westerfield (1985), Sias and Starks (1995), Ariel
(1990), and Wang, Li, and Erickson (1997), which have documented discov-
eries relating to the weekend effect. These and Fosback (1986), Damodaran
(1989), Kamstra, Kramer, and Levi (2000), Dyl and Martin (1985), Lakonishok
and Levi (1982), Chang, Leung, and Wang (2003), and Chen and Singal (2003)
examine potential explanations of the weekend effect.
2. Since Mondays follow days that are closed for trading, the Monday return
should actually reflect the return for more than one day and, therefore, should
be greater than the return on other days. Thus, the weekend effect should be
negative for all securities.
3. See Appendix B for a discussion on short selling.
4. Under the uptick rule, an investor cannot short sell shares of a stock that is
falling in price.
5. Since price volatility over nontrading hours is much smaller than during trad-
ing hours, it can be argued that nontrading hours are less important than trad-
ing hours in terms of volatility. However, note that as short sellers can monitor
prices during trading hours and take action, the volatility during trading hours
is inconsequential, even desirable. On the other hand, even a little volatility
during nontrading hours can be devastating to the short sellers.
Beyond the Random Walk56
Events associated with high-quality information signals tend to exhibit
price continuations. The quality of information is characterized by the
magnitude of price change, volume, and public dissemination of infor-
mation. There is evidence to suggest that a large price change accom-
panied by high volume and a public announcement is followed by a
drift in prices. A trading strategy designed to capture this short-term
price continuation will earn annual abnormal returns of 15–36 percent
after transactions costs.
Predictably, there is much research on price continuations (also called
price drift or price momentum) and price reversals.1
It seems that
there is momentum in stock returns over periods of six to twelve
months—that is, if prices are rising, they will continue to rise, or if
they are falling, they will continue to fall (see Chapter 5). Over longer
periods extending up to five years, there is a tendency for mean
reversion, that is, prices revert to normal levels. The medium- and
long-term evidence suggests that there are cycles in price patterns.
However, mispricings that rely on long periods are not interesting.
First, it is not clear that those mispricings actually occur, given the
noise in estimates. Second, trading strategies are not easily ame-
nable to long holding periods.
Short-term price patterns considered here are of two kinds: the
pattern could be a form of price drift, where the price continues to
move in the same direction, or it could be a price reversal where the
Short-Term Price Drift
Short-Term Price Drift 57
price moves in the opposite direction. These price patterns may be
due to market frictions, a result of market inefficiency, or related to
The earliest documentation of short-term price drift is related to
earnings announcements, in which it was found that firms with sur-
prisingly good earnings earn abnormal returns of about 2 percent
in the following three months, whereas firms with surprisingly bad
earnings lose abnormally. Evidence of price drift suggests that in-
formation in the earnings announcement is not immediately and
fully reflected in prices. Other research has found that trading vol-
ume is important in evaluating the permanence of price changes.
Stock prices, especially of inactively traded stocks, can be affected
by medium-sized trades that do not contain any new information.
A sell order driven only by a need for cash can push down the price
artificially that reverses over the next few days. The type and qual-
ity of information determine whether the price impact is perma-
nent or temporary.
What is information quality and how can it be measured? The
quality of information signals can be measured on different dimen-
sions: magnitude, precision, and dissemination. The first dimen-
sion, the size of a price change, captures the magnitude of the signal
or the significance of the news. The second dimension is precision
of information quality, which is measured by volume. If the infor-
mation is precise, then more people are likely to trade as they rebal-
ance their portfolios or take new positions in response to the new
information. Finally, the third dimension of information quality is
dissemination of new information and is determined by whether or
not a public announcement is made. Since public announcements
are more credible due to legal and reputation costs, they are likely
to contain higher-quality information. However, any one of the prox-
ies used captures only one of the three dimensions. Using all three
quality-identifying proxies simultaneously should improve the de-
tection of price patterns.
The idea is that if a stock experiences a large price change unac-
companied by high volume or a public announcement, then that price
change may get reversed. On the other hand, a price change accom-
panied by high volume and a public announcement is likely to be
permanent. Indeed, if large price changes are accompanied by an in-
crease in volume and a public announcement by the management or
analysts, then a price continuation is likely to result in a one-month
abnormal return of about 3.5 percent for positive events and –2.25
percent for negative events. Atrading strategy set up to exploit these
price patterns can earn an abnormal return of 1.25 percent to 3 per-
cent after transaction costs, that is, 15–36 percent annually.
Beyond the Random Walk58
The evidence on the short-term price drift begins with a large price
change as an indicator of a strong signal of new information. Alarge
price change (stock return) can be defined in two different ways: as
an absolute return or as a relative return. A 10 percent absolute re-
turn or a change in price from $50 to $45 (or to $55) obviously seems
like a large price change. However, a 10 percent return in one day
may be relatively common for riskier stocks, such as technology
stocks. For example, Amazon.com’s price changed by more than 10
percent fourteen times over the July 2001–June 2002 period. By com-
parison, General Electric’s return crossed the 10 percent threshold
only two times during that period. Further, the 10 percent limit be-
comes easier to cross for a stock with a price of less than $1 because
a change of 10 cents in the price translates into a 10 percent return.
ICGE, a stock with a price of less than $1, earned or lost more than
10 percent in a day forty-five times in a one-year period.
Due to the limitations of an absolute return, a relative return seems
more appropriate. For one thing, the relative return criterion does
not impose an ad hoc cutoff that is invariant across different kinds
of stocks; rather, the threshold of relative return is based on the nor-
mal return and its volatility. In other words, if relative return is used
to select large returns, then the top 1 percent of all returns, ignoring
the sign, will be considered large for a particular stock.2
ing the top 1 percent of 250 daily returns of a stock (there are 250
trading days in a year) means that the top two or three returns ev-
ery year are large. Continuing with the stocks considered in the pre-
vious paragraph, the two 10 percent returns for GE will be
considered large, constituting the greatest 1 percent of all returns.
For Amazon.com, only three of the fourteen returns fall in the top 1
percent category. For ICGE, three of the forty-five returns fall in the
top 1 percent category. The advantage of using the relative return
screen is that the selected sample will represent all firms equally,
unlike the absolute return criterion, which is geared toward select-
ing more stocks that are riskier or low-priced. The disadvantage is
that the relative return is different for each stock and requires com-
putation for each individual stock to judge whether or not a par-
ticular return falls in the top 1 percent of all returns.
RESULTS WITH LARGE PRICE CHANGES
Results presented in Table 4.1 are for all large price changes. The
relative return criterion for the first two returns requires that the
Table 4.1 Price Continuations and Reversals Following Large Price Changes
Selection Return Abnormal
Criterion on Day Return:
for of Large Day 1
Sample Return on Market Price Volume Change to
Period Size Day 0 Adjusted Level Requirement (Day 0) Day 20
1. 1990–1992 2,919 Relative return Yes >$10 Yes 7.13% 0.08%
2. 1990–1992 1,954 Relative return Yes >$10 Yes –7.13% –0.48%
3. 1984–1987 1,276 >10% Yes >$10 — 12.31% –2.13%
4. 1984–1987 840 <–10% Yes >$10 — –13.83% –1.12%
Abnormal return is defined as the raw return minus the S&P 500 return for a particular day. Event day is the day of the large price change. Sources: Pritamani and
Singal (2001), Park (1995), and Cox and Peterson (1994).
Beyond the Random Walk60
selected return be an extreme price change for the firm that lies more
than three standard deviations away from the mean. This means
that approximately 0.25 percent of all returns for a particular stock
are selected. The day on which the large price change occurs is re-
ferred to as day 0 or the event day.
The other conditions imposed for initial selection are also impor-
tant. First, all returns are adjusted for the market. Imagine a day
when the market falls by 5 percent. A large number of companies
will fall in value, though the reason for the fall does not relate to the
individual firm. Accordingly, an adjustment for market return is
made before selecting firms.
One big concern with short-term drift is that patterns discovered
may not represent a mispricing; rather, they may represent the bid-
ask bounce (also see “Alternative Explanations” in Chapter 3). For
example, consider a stock (say, ICGE) that trades at less than $1.00 a
share. On a large price change day, assume the price falls from $0.60
with a closing bid price of $0.50 and a closing ask price of $0.51.
Assume that the last trade on day 0 occurs at $0.50; that translates
into a fall of 16.7 percent from a previous price of $0.60. Next day
(day 1), nothing changes and the bid and ask prices remain at $0.50
and $0.51. If the last trade is a buy that takes place at the ask price of
$0.51, the recorded closing price would be $0.51, which is an in-
crease of 1 cent and a calculated return of 2 percent. Looking at the
closing prices alone, it seems reasonable to conclude that there is a
reversal following large price changes (–16.7 percent on day 0 fol-
lowed by +2 percent on day 1), though nothing actually changed
between day 0 and day 1. On the other hand, assume that the price
falls from $0.60 to $0.51 on the event day, a drop of 15 percent.Again,
assume that nothing changes on day 1, but the last trade is executed
at the bid price of $0.50, a drop of 1 cent and a return of –2 percent.
Now it seems reasonable to conclude that there is a continuation—
a fall of 15 percent is followed by another fall of 2 percent on the
next day. Though the assumptions about ICGE’s stock price sug-
gest that there is no change, the return calculations reveal a pattern
because of closing trades bouncing between the bid and ask prices.
To guard against spurious results due to the bid-ask bounce, a
$10 price limit is imposed. However, many stocks with a price of
more than $10 can also have large bid-ask spreads. For example,
Masonite International (NYSE: MHM) has a price of more than $10,
but the bid-ask spread is about 1 percent. Also, imposing an addi-
tional condition of nonzero volume on any day can reduce the in-
clusion of infrequently traded stocks. Moreover, trading strategies
will not work effectively with stocks that have large bid-ask spreads.
Short-Term Price Drift 61
Instead of using objective criteria to screen stocks, it is significantly
more effective just to make sure that stocks with a high cost of trad-
ing are not included in trading strategies.
Accordingly, stocks considered in Table 4.1 have a lower price
limit and, in some cases, a minimum volume requirement. From
the table, you can see that there are no consistent patterns. The ab-
normal return (raw return adjusted for the market) over 20 trading
days is only 0.08 percent in the first row, –0.48 percent in the second
row, a reversal of –2.13 percent in the third row and a continuation
of –1.12 percent in the fourth row.3
Thus, overall, for large price
increases and declines, there is no evidence of a price drift.
RESULTS WITH LARGE PRICE CHANGES AND HIGH VOLUME
The second distinguishing feature of information quality is its pre-
cision. As the signal becomes more precise, it will lead investors to
have more confidence in their valuation of the stock, and so they
will be more willing to make large trades. For example, if a com-
pany announces surprisingly good earnings and high revenues and
forecasts stronger results in the future, the investors are likely to
believe that the stock’s valuation should be higher, leading to active
trading in that stock and significantly higher volume. On the other
hand, postings on Internet message boards promoting a particular
stock may not instill much confidence. Though the price might rise
due to the trades of few people on low volume, especially in illiq-
uid stocks, it is just as likely to fall quickly on subsequent days.
Volume is, therefore, generally viewed as an effective measure of
information precision. In the same vein, chartists usually look at
volume to confirm price trends. Price changes unaccompanied by
high volume are considered suspect and require further review.
Financial news services routinely report up-volume and down-
volume to give an indication of the strength of market moves.
Just like with return, defining high volume becomes a challenge.
The results presented in panel A of Table 4.2 assume that the trad-
ing volume on day 0 is in the top 10 percent of daily volumes over a
sixty-day period, that is, among the top six volume days. Since an
individual stock’s volume, like its return, depends on market vol-
ume, it is appropriate to adjust the stock’s trading volume by mar-
The results in panel A of Table 4.2 reveal two return patterns.
First, price changes that are accompanied by high volume have price
continuations. Price increases with high volume are followed by
subsequent increases of 0.20 percent and 0.95 percent over five-day
Beyond the Random Walk62
and twenty-day periods. Similarly, price decreases with high vol-
ume are followed by further price decreases of 0.66 percent and 0.65
percent in the five-day and twenty-day periods. Price changes not
accompanied by high volume have a slight reversal in returns.
RESULTS WITH LARGE PRICE CHANGES, HIGH VOLUME, AND NEWS
The third characteristic of signal quality is dissemination of infor-
mation, proxied by announcement of the information. The primary
source of information about a company is the company itself. Offic-
ers of a company cannot legally trade on material nonpublic infor-
mation (see Chapter 7, on insider trading). Instead, the company is
encouraged to make public any material information as soon as
possible. That is why companies routinely preannounce their earn-
ings estimates if they are significantly different from publicly avail-
able information. Security analysts can also generate new information
based on their own reading of the industry or that particular firm.
But their analysis is derived from information disclosed in corpo-
rate news releases. Analysts can, of course, choose not to publicly
release their recommendations, as they are not subject to insider
trading laws, provided that their analysis is based on publicly avail-
Table 4.2 Returns Following Large Price Changes, High Volume, and News
Price High Public Sample Days 1–5 Days 1–20
Change Volume News Size (%) (%)
Panel A: Large price changes with and without high volume
1. Increase Yes — 1,477 0.20 0.95
2. Increase No — 1,442 –0.71 –0.67
3. Decrease Yes — 1,142 –0.66 –0.65
4. Decrease No — 812 0.49 –0.13
Panel B: Large price changes, high volume, and public news
5. Increase Yes Yes 603 0.54 1.98
6. Increase Yes No 874 –0.09 0.03
7. Decrease Yes Yes 653 –1.26 –1.68
8. Decrease Yes No 489 0.63 0.52
Large price change is based on relative return. The return must lie more than three standard
deviations away from the mean return calculated over the last one year. A stock is deemed to
have a high volume if its volume on the event day lies in the top 10 percent of daily volumes
over the previous sixty days. Abnormal return is defined as the raw return minus the S&P 500
return for that day. The event day is the day of the large price change. Source: Pritamani and
Short-Term Price Drift 63
able information. On the other hand, analysts do have an incentive
to publicize their recommendations because correct calls will en-
hance their reputation in the market. Thus, analysts will usually
choose to publicize rating changes in which they have confidence,
notwithstanding calls by Merrill Lynch’s Henry Blodget on Internet
stocks and Salomon Smith Barney’s Jack Grubman on the telecom
Large price changes can also occur in the absence of new infor-
mation. For example, an institution may decide to trade a particular
stock for portfolio rebalancing, selling it if it has become over-
weighted due to price appreciation or buying it if it has become
underweighted due to a fall in the stock price. Or a large shareholder
may sell a significant fraction of his shareholding because he needs
the cash to diversify into real estate or buy an executive jet.
As these events contain no new information about the stock, they
are unlikely to provide reliable predictions about price movements
and should be excluded from further consideration. Results are pre-
sented with and without public news for comparison in panel B of
Table 4.2. It can be seen that the distinction between the news sample
and no-news sample is quite sharp. There is a definitive continua-
tion in returns when price changes are accompanied by high vol-
ume and public news: price increases are followed by an increase of
1.98 percent in the subsequent twenty trading days, while price
decreases are followed by a return of –1.68 percent. On the other
hand, there is no pattern when price changes are not accompanied
by a public announcement.
TYPE OF NEWS
The type of news is important to judge the probability of a price
drift or momentum. Extremely precise information may not neces-
sarily provide an opportunity to predict future movements in price.
Cash mergers are one such case. For example, Regions Financial
Corp. announced a cash bid for Morgan Keegan (NYSE: MOR) on
December 18, 2000, at $27 per share (see Chapter 11, on merger arbi-
trage). The price of MOR jumped 35 percent to close at $26.13 on a
volume of 576,400 shares, compared to a normal daily volume of
less than 50,000 shares. The next highest volume in the prior three
months was 113,600 shares. This particular instance meets the re-
quirements for inclusion in the sample. However, there is no uncer-
tainty about the target’s price, assuming the merger is successful.
Not surprisingly, the price moved within a narrow range of about 1
percent over the next several days.
Beyond the Random Walk64
On the other hand, Intel warned about impending underper-
formance after the close on June 6, 2002. The next day Intel fell from
$27 to $22, a decline of 18.5 percent, on a volume of 152 million shares.
The price change and the volume were among the highest ever. In
spite of the announcement, there was great uncertainty about Intel’s
correct valuation. It seems obvious that if the preannouncement price
of $27 was correct, the correct postannouncement value must be
below $27. But the question is whether it should be $25, $20, $10, or
$5. The price uncertainty surrounding big news is ideal for price
continuations. Indeed, Intel’s price fell by 12.1 percent over the next
twenty days, while during the same period the Nasdaq 100 fell by
6.9 percent and the S&P 500 fell by 3.8 percent. Thus, Intel under-
performed the market by at least 5.2 percent.
The implication for price drift is obvious from the two examples—
that the type of news matters. The results for different kinds of news
are given in Table 4.3. Actual earnings announcements or pre-
announcements by the management and analysts’ reports are the
most effective predictors of price drift. The abnormal returns after
these public announcements can be large: about 1 percent within
five trading days and 3.50 percent over twenty trading days after
large price increases, and about –2.4 percent over twenty days after
price decreases. Other news items have no predictive power in the
case of positive events, though there is a price drift for negative
events. A possible reason for this difference is discussed in the next
paragraph. The abnormal returns have already been adjusted not
Table 4.3 Price Continuations Conditional on News Type
Price High News Sample Days 1–5 Days 1–20
Change Volume Type Size (%) (%)
1. Increase Yes Earnings 226 1.03 3.50
2. Increase Yes Analysts’ 102 0.80 3.59
3. Increase Yes Others 243 0.04 0.08
4. Decrease Yes Earnings 337 –1.58 –2.37
5. Decrease Yes Analysts’ 217 –1.11 –2.39
6. Decrease Yes Others 318 –1.08 –0.44
Large price changes are based on relative return. The return must lie more than three standard
deviations away from the mean return calculated over the last one year. A stock is deemed to
have a high volume if its volume on the event day lies in the top 10 percent of daily volumes over
the previous sixty days. Abnormal return is defined as the raw return minus the S&P 500 return
for that day. Event day is the day of the large price change. Source: Pritamani and Singal (2001)
Short-Term Price Drift 65
only for the market in general but also for the particular firm’s risk.
So the risk adjustment is superior to a normal adjustment. How-
ever, it is known that firm risk normally increases around extreme
events. The returns in Tables 4.1, 4.2, and 4.3 do not account for any
additional event-related risk.
One interesting observation appears from a comparison between
large price decreases and large price increases: the limitations im-
posed by short sales. In the case of large price increases, other types
of news have no residual effect after the event day (see row 3 in
Table 4.3), that is, all of the information is incorporated right away
on the event day. However, in the case of large price declines, other
types of news continue to impact the stock, as much as 1 percent in
the first five trading days after the event (see row 6 in Table 4.3).
Why does this difference exist? A natural reason for the difference
is the cost of short selling. Consider IBM’s surprisingly good earn-
ings reported after the close of the market on October 16, 2002. Any-
one who wanted to buy IBM as a result of this report could buy the
stock. The current holders of IBM could buy more, and investors
who did not own IBM could also buy IBM stock. On the other hand,
consider AOL Time Warner’s revelation of a fact-finding inquiry by
the SEC into its accounting practices on July 24, 2002 (a negative
event). Investors who owned AOL could sell the stock if they so
desired. However, the only way investors who did not own AOL
Price Continuation After Earnings Surprises
Day 0 Day 1 Day 5 Day 10 Day 15 Day 20
Figure 4.1 The day of the surprise announcement is day 0. The price drift over the
twenty-day period after the announcement is shown in the figure for firms with large
price increases, high volume, and a public earnings announcement.
Beyond the Random Walk66
stock could trade on this information was by short-sellingAOLstock.
As explained in Appendix B, it is difficult and expensive to short-
sell. Therefore, the price drift in stocks following large price declines
may extend over a longer period than the price drift in stocks fol-
lowing large price increases.
The results in Tables 4.1 to 4.3 do not consider the costs of trading. It
is necessary to obtain an estimate of trading costs to accurately esti-
mate realizable profits. The primary component of trading costs is
the bid-ask spread. Brokerage commissions are usually negligible
and there is not likely to be any significant price impact, as a typical
investor’s trade is small. On average, the bid-ask spread is about
0.5 percent. Therefore, the net abnormal return after trading costs
will be about 3.0 percent over a twenty-day period following large
price increases, or about 36 percent annually. In the case of price
declines, the total cost of trading may be about 1.0 percent, as the
trading strategy will entail short sales. Thus, the net abnormal re-
turn after trading costs is estimated to be about 1.4 percent follow-
ing large price declines, or 16.8 percent on an annual basis.
Evidence related to short-term price drift seems quite compelling.
Moreover, price drift following earnings announcements (but not
conditioned on volume or price changes) has been known to exist
since the mid-1980s. Why did the short-term price drift continue to
persist even in the late 1990s and continue today? Four possible
explanations are discussed below.
First, information seems to come in cascades, that is, good infor-
mation is followed by more good information, and bad information
by more bad information. The assumption of cascades in informa-
tion is not necessarily unreasonable. Positive earnings surprises are
usually followed by analyst upgrades, while negative earnings sur-
prises are followed by analyst downgrades. For example, Intel’s
warning on June 6, 2002, was quickly followed by downgrades by J.
P. Morgan and CIBC World Markets. Morgan Stanley removed Intel
from its Fresh Money list on June 11. On the same day, June 11, Intel
followed up by reporting that its earnings visibility was impaired
and the current environment was not good. On June 12, an analyst
firm reported that there was an excess inventory of PC mother-
Short-Term Price Drift 67
boards. Thus, in Intel’s case, an initial warning is followed by recur-
ring bad news over the next several days; in some situations there is
new information, while in others old information is repackaged and
presented in a different forum or through a different medium. If the
assumption of cascading information is correct, prices might ex-
hibit the momentum reported in the previous section.4
The second explanation for the price drift is related to strategic
trading by large institutional investors. As institutions must trade
large parcels of stock to significantly change their portfolios, they
are concerned about how their trades will affect the price. Though
the daily trading volume of many stocks runs into millions of shares,
the stock price will still be negatively affected if an institution wants
to sell several million shares of the stock and will be positively af-
fected if the institution wants to buy the stock. Therefore, in order
to minimize the price impact of their trades, institutions strategi-
cally divide their entire order into several smaller trades spread over
one or many days. As repeated buy orders (or sell orders) appear in
the market, they are likely to pressure the price to move up (or
down). Large price changes considered in this chapter can become
important events for investment portfolios triggering rebalancing
of the portfolio because the price target has been reached, the stock
is no longer worthy of inclusion in the portfolio, or the institution
decides to buy the stock because its upside potential has improved.
Thus, strategic trading by institutions may cause the observed price
The third explanation suggests that short-term price drift actu-
ally does not exist once the risk of the event is considered. If the
stock becomes riskier around an event because of greater uncer-
tainty, it must earn a higher return as compensation for that risk.
The returns in Tables 4.1 to 4.3 do not explicitly account for higher
risk around public announcements. This explanation, however, has
two shortcomings. First, the return that can be earned (3 percent in
one month) is too high as compensation for typical estimates of
event-related risk. Most risk-averse investors will find the excess
return very attractive. Second, the explanation requires a positive
return after both positive and negative events in order to compen-
sate for the extra risk. The continuation of the negative price drift
after price declines is inconsistent with this explanation.
Finally, prices may not react fully to new information because of
investor behavior (see Chapter 12 for a discussion). As investors are
slow to change their deeply held beliefs about a stock’s value, they
tend to underreact. According to this explanation, as investors real-
ize their mistakes, they trade, but with a time lag, resulting in the
Beyond the Random Walk68
price drift. In addition, investors are averse to selling at a loss and
will continue to delay selling in the hope that the stock price will
recover. As a result of this characteristic of investor behavior, the
negative drift in price would be less than the positive drift in price.
This prediction is supported by the data in Table 4.3.
Whether the price drift occurs due to strategic trading, informa-
tion cascades, or irrational investor behavior, it is reasonable to claim
that the drift will continue to persist.
The Trading Process
The process of identifying potential candidates for the trading strat-
egy requires an analysis of all stocks at the end of the day based on
closing prices by applying different criteria that have generated
abnormal returns in the past. The trading strategy described below
covers both large price increases and large price declines, though
most investors would want to concentrate on the large price increase
sample since it does not require short selling and is potentially more
Step 1: The first step is to pick stocks that experienced a large
price change. As mentioned in “Evidence,” earlier in the chapter, a
large price change can be defined as an absolute return or a relative
return. A 10 percent cutoff is deemed adequate to select stocks on
an absolute basis. Implementation of the relative return criterion
becomes difficult because each stock has its own cutoff. However,
to make it simple, the relative return criterion can be combined with
an absolute return screen. For example, first, all stocks that experi-
enced a change of at least 5 percent are selected. Second, for each
such stock with a return of at least 5 percent, the relative return
criterion is applied by checking whether that day’s return (ignoring
the sign) falls in the top three returns for the year for that stock.5
This process is performed at the end of each trading day.
Step 2: For the selected sample of stocks, stocks whose stock price
is less than $10 before the large price change are excluded. In addi-
tion, it should be ensured that the same stock is not selected in the
previous month, as this large price change should not be a continu-
ation of an earlier price change.
Step 3: The second screen is related to volume. Exclude the firm if
the stock’s event day volume does not fall in the top 10 percent of
daily volumes over the past sixty trading days. If it does, make sure
that it still constitutes one of the six highest daily trading volumes
when adjusted for market volume on the event day. Some data
Short-Term Price Drift 69
sources do not adjust the trading volume for stock splits. Check for
any stock splits in the last three months and, if necessary, adjust the
volume for the splits.
Step 4: The third screen is related to public announcement of news.
The easiest way to look for news is to use the ticker symbol and type
it into news services’ search box. The news about the stock should be
related to earnings announcements, earnings preannouncements,
distributions, or analyst ratings of stock or debt. While earnings an-
nouncements by the management will be carried by all news ser-
vices, some analyst ratings are first announced to their customers
before being disseminated in the media. In any case, if no news item
related to the stock can be found then drop that stock from the sample.
Step 5: Before placing trades for selected stocks, it is important to
ensure that there are no company announcements scheduled for
the twenty-day holding period after the event day. Scheduled an-
nouncements will unnecessarily increase the risk of the position, as
the announcement can have a large positive or negative effect on
the company’s stock price.
Step 6: For stocks that experience large price increases, put in an
order to buy at the opening price. For stocks that experience large
price declines, put in an order to short-sell with the limit price set to
the previous day’s close.
Step 7: Four weeks (or twenty trading days) later, close all open
The process described above is actually employed in this section
for the month of April 2002. For each day in April, an initial set of
stocks is chosen from the Quotes-Plus database (see “Historical Price
Data” in this chapter for details) that satisfy the following condi-
tions: it is a common stock, it traded a minimum of one thousand
shares on the previous trading day, and it earned a return of at least
5 percent plus the S&P 500 return for that day. The number of stocks
selected, by day, is shown in column 1 of Table 4.4. On each day
there are more than five hundred stocks that earned an abnormal
return of more than 5 percent. Introducing the $10 price limit cuts
the number of stocks to about one-quarter the original number. High
volume and high return are the next two screens. In addition, the
large price change must not be a continuation from another recent
event. In other words, the current event must be the first eligible
event over the prior twenty days. On average, only five or six stocks
Table 4.4 Stock Selection for April 2002
Number of increase Number of decrease
Date Column 1a
increases (%) decreases (%)
April 1, 2002 631 128 32 7 2 1 17.4 1 –52.1
April 2, 2002 600 166 50 16 4 0 — 4 –19.0
April 3, 2002 509 122 33 5 2 0 — 2 –13.5
April 4, 2002 501 122 48 18 8 4 9.2 4 –20.9
April 5, 2002 513 105 38 12 5 3 11.0 2 –13.9
April 8–29, data not shown
April 30, 2002 785 176 51 10 2 2 10.3 0 —
Total for April 13,089 3,436 1,250 301 114 55 12.9 59 –16.9
Column 1 = Stocks with volume 1,000 and absolute abnormal return of at least 5 percent.
Column 2 = Column 1 + the price on the day before the event is greater than $10.
Column 3 = Column 2 + volume in the top 6 out of previous 60 days.
Column 4 = Column 3 + return in the top three among the last year.
Column 5 = Column 4 but excluding continuations of earlier events.
The original data set is from Quotes-Plus.
Short-Term Price Drift 71
satisfy these criteria each day. The total number of events selected
for April 2002 is 114, including 55 price increases and 59 price de-
clines. The average price increase is 12.9 percent on the event day,
while the price decrease is –16.9 percent.
The selected stocks are further refined by searching for the type of
news. Since April follows the quarter end in March, a large fraction
of the large price changes can be attributed to earnings announce-
ments. Thirty-two earnings announcements and preannouncements
account for price increases, while thirty-nine are responsible for price
declines. Announcements of distributions by the company fall into
the same category as earnings announcements, though they are cat-
egorized differently in Table 4.5. There are eight rating changes by
security analysts. These rating changes are not concurrent with or
close to a corporate announcement. Finally, no news is found for
twenty-four large price changes. Absence of news could be related
to aggressive trading by an institution based entirely on its own
assessment of the stock. Or it could be because analyst recommen-
dations are disclosed only to the company’s clients and not to other
investors. Finally, the media may not have carried the news if the
company is too small or if the news services did not consider the
news important enough.
RESULTS BY NEWS TYPE
The returns by news type for April 2002 are in Table 4.6. Announce-
ments by the company that pertain to the company’s financial per-
formance (types 1 and 3) are reported in the first column. For the
thirty-five stocks, the mean abnormal return is 3.36 percent over a
twenty-day period after the large price increase. Two-thirds of the
positions are winners. The costs of transacting have not been ex-
plicitly considered. As these stocks have an average price of $32
and are traded actively on days around the event, the bid-ask spread
is unlikely to be more than 0.50 percent. Thus, the net return is 2.86
percent per month, or 34 percent annually.
The price drift after large price declines is similar. The sample
firms lose 4.27 percent over the following twenty trading days. Ad-
justed for the market, the mean abnormal return is computed as
–1.67 percent. As mentioned earlier, the trading strategy in the case
of large price declines entails a short position. Therefore, the –1.67
percent actually reflects a gain of 1.67 percent. Considering 1 per-
cent as the cost of a short sales transaction, the net profit is only 0.67
Table 4.5 Type of News Announced for Selected Firms in April 2002
Type of Number Number Included Price Price
News Description of Firms in Final Sample Increases Decreases
1 Actual earnings 71 71 32 39
and earning forecasts
2 Analyst ratings not related 8 8 3 5
to type 1
3 Distributions 3 3 3 0
4 Legal actions 1 0 0 1
5 Accounting-related 3 0 0 3
6 Pharmaceutical trials 1 0 0 1
7 News followed by 2 0 0 2
8 No news 24 0 17 7
9 Miscellaneous 1 0 0 1
Total 114 82 55 59
News items are searched on Bloomsberg.com’s news archive, Briefing.com, and Bigcharts.com.
The news types are defined as follows:
News type 1: Earnings announcement or preannouncement by the company.
News type 2: Rating upgrade or downgrade by security analysts. The rating changes must not be in response to earnings announcements.
News type 3: Distribution announced by the company, such as a cash dividend or stock split, but not concurrent with news type 1.
News type 4: Legal actions initiated or concluded against the company.
News type 5: Any accounting irregularities disclosed by the company or alleged by a government agency.
News type 6: News related to the progress of pharmaceutical trials or application to the FDA.
News type 7: News that is immediately (one to two days) followed by a scheduled earnings announcement.
News type 8: No news found in the news services listed or on the company’s website. However, this does not mean that there was no news—only that none could
News type 9: Miscellaneous, not elsewhere classified. In this case, it is a complaint to the FCC.
Short-Term Price Drift 73
percent.As shown in Table 4.3, the lower profitability after large price
declines is not unexpected. Moreover, the median abnormal return is
positive, and only 49 percent of the positions are winners. Given the
evidence in Table 4.3, the evidence in Table 4.6 for April 2002, and
the difficulty in short selling, it is probably best to exclude stocks
with large price declines while constructing a trading strategy.
News type 2 refers to rating changes by analysts. If a rating change
occurs concurrently with an earnings announcement, the news is clas-
sified as type 1. Thus, these rating changes are isolated events usu-
ally far removed from any other significant news related to the
company. News about changes in analyst ratings has the most sig-
nificant price drift, at least for the stocks selected in April 2002. The
mean return is 7.53 percent following large price increases and –10.63
percent following large price declines. Though the sample size calls
for caution, the returns are large and attractive.
Other news items—accounting irregularities, legal problems, and
progress of pharmaceutical trials—are announced only for price de-
clines. These news releases result in an overreaction for the month
of April 2002.
Table 4.6 Returns for Stocks Selected in April 2002, by News Type
Earnings and Analysts’ No
Distributions Ratings News
Panel A: Price Increases
Sample size 35 3 17
Event day return 13.2% 19.5% 11.1%
Average stock price $32 $27 $26
20-day raw return 1.03% 4.75% 1.27%
20-day S&P 500 return –2.33% –2.78% –3.52%
Mean abnormal return 3.36% 7.53% 4.78%
Median abnormal return 2.99% 15.27% 2.76%
Percent positive 66% 67% 76%
Earnings and Analysts’ Other No
Distributions Ratings News News
Panel B: Price Decreases
Sample size 39 5 7 7
Event day return –17.8% –11.0% –18.1% –15.5%
Average stock price $26 $22 $22 $24
20-day raw return –4.27% –12.98% 1.92% –4.50%
20-day S&P 500 return –2.60% –2.35% –1.07% –1.77%
Mean abnormal return –1.67% –10.63% 2.99% –2.73%
Median abnormal return 0.49% –12.34% 6.84% –6.20%
Percent negative 49% 100% 29% 71%
News items are searched on Bloomsberg.com’s news archive, Briefing.com, and Bigcharts.com.
Beyond the Random Walk74
Surprisingly, the no-news sample (type 8) also exhibits signifi-
cant price drift: an average of 4.78 percent following price increases
and –2.73 percent following price decreases. There are two possible
explanations. First, the media did not carry information about the
companies, though that information was important. Second, the
month of April 2002 just happens to be different from other months.
Nonetheless, the primary evidence of price drift following large
price changes in section 4.2 is reconfirmed by the results for April
2002. Relying on large price increases due to announcements by the
management and analyst rating changes would have generated an
average abnormal return of 3.19 percent (average of returns to types
1, 2, and 3) over a twenty-day period following large price increases,
or an annualized return of 38 percent.
Annualized returns are used for a better understanding of the
magnitude of gains. To annualize the abnormal return calculated
above, it is assumed that the same return can be earned for multiple
events in a sequential manner. For example, if an abnormal return of
5 percent is earned over a period of twenty trading days, it is as-
sumed that we will earn the same 5 percent abnormal return in sub-
sequent twenty-day periods. Thus, the annualized return is calculated
simply as the 5 percent abnormal return times 12, since there are 250
trading days in a year or approximately twelve twenty-day periods.
The evidence and the trading strategy recommendations presented
in this chapter are based on past data. Since future market condi-
tions and market patterns may be completely different, there is no
certainty that the short-term price drift will continue in the future
or be profitable.
In addition, all of the evidence suggests positive abnormal re-
turns. However, even with positive abnormal returns, one might
lose money if the market return is sufficiently negative. It is known
that there is an increase in risk around important events. While the
abnormal returns have been adjusted for normal levels of risk, they
do not account for heightened event-related risk. Finally, hedging
against market movements with S&P futures is appropriate to re-
duce one’s risk and increase the chances of earning the abnormal
returns documented here.
Short-Term Price Drift 75
• Do prices exhibit any patterns after large price changes? Is there
an overreaction or an underreaction? It seems that the discov-
ery of patterns depends on the quality of information. Quality
of information is proxied by price changes, volume, and news.
• The evidence reveals that there is no predictability in returns
following large price changes. However, the returns become
predictable if the price changes go together with extraordinar-
ily high volume. Announcement of public news further im-
proves the reliability of forecasts. For different types of news,
price changes following earnings announcements and analysts’
reports can continue to drift over the next twenty days. The
annualized abnormal return is approximately 36 percent fol-
lowing large price increases and 18 percent following large price
• The explanations for this phenomenon are varied. There has
not been much research aimed at explaining short-term price
drift. One of the possibilities is information cascades, that is,
good information is followed by more good information be-
cause information comes in bits and pieces. Another explana-
tion is based on strategic trading by institutions. As institutions
must trade large quantities, they break their orders into small
parcels to reduce the price impact. Irrational investor behavior
could be another reason if investors are slow to sell their losers
and quick to sell their winners causing prices to drift for sev-
• Atrading strategy can be devised and applied to real data. The
strategy reveals an abnormal return of 38 percent per year by
capturing the drift following large price increases in the month
of April 2002. The success ratio is 66 percent.
In general, there is no evidence of tradable price regularities follow-
ing large price events. If large price changes are accompanied by
other traits of information, such as high volume and public dissemi-
nation of news, the patterns become stronger. Evidence of price con-
tinuation becomes very important for news relating to earnings,
distributions, and analyst recommendations, where the postevent
Beyond the Random Walk76
twenty-day price drift is +3.50 percent for positive events and –2.25
percent for negative events. The annualized return after transac-
tions costs can be estimated at 36 percent annually for positive price
changes and 15 percent for negative price changes. This strategy
works even in bear markets!
Historical Price Data
http://www.qp2.com: Quotes-Plus contains all stocks traded on NYSE, AMEX,
and Nasdaq. It provides daily updates.
http://www.fasttrack.net, http://www.msodata.com: These are some other
sources that provide data needed for this chapter.
http://www.bigcharts.com: Very comprehensive site—one is more likely to
find a press release on this site than anywhere else. However, the site does
not contain information about announcements that are not publicly released,
such as some rating changes. For those types of news, Briefing.com is better.
In addition, the site does not provide information carried exclusively by
http://www.briefing.com: Abridged news articles are available for most
companies and for several years in a nice accessible format. Requires a
http://www.newsalert.com: News articles up to three months old are available.
http://online.wsj.com: Articles up to thirty days old are available without extra
payment. Requires a subscription.
http://finance.lycos.com, http://finance.yahoo.com, http://www.newsedge.com:
These sites contain news from all major news services but do not archive
References for Further Reading
Chan, Wesley S. 2003. Stock Price Reaction to News and No-news: Drift and Re-
versal After Headlines. Journal of Financial Economics, forthcoming.
Cox, Don R., and David R. Peterson. 1994. Stock Returns Following Large One-
Day Declines: Evidence on Short-Term Reversals and Longer-Term Perfor-
mance. Journal of Finance 49, 255–67.
Fehle, Frank, and Vladimir Zdorovtsov. 2002. Large Price Declines, News, Liquid-
ity, and Trading Strategies: An Intraday Analysis. Working paper, Department
of Finance, University of South Carolina.
Larsen, Stephen J., and Jeff Madura. 2003. What Drives Stock Price Behavior Fol-
lowing Extreme One-Day Returns. Journal of Financial Research 26(1), 129–46.
Nofsinger, John R. 2001. The Impact of Public Information on Investors. Journal of
Banking and Finance 25, 1139–366.
Short-Term Price Drift 77
Park, Jinwoo. 1995. A Market Microstructure Explanation for Predictable Varia-
tions in Stock Returns Following Large Price Changes. Journal of Financial and
Quantitative Analysis 30, 241–56.
Pritamani, Mahesh, and Vijay Singal. 2001. Return Predictability Following Large
Price Changes and Information Releases. Journal of Banking and Finance 25(4),
Ryan, Paul, and Richard J. Taffler. 2002. What Firm Specific News Releases Drive
Economically Significant Stock Returns and Trading Volumes? Working pa-
per, School of Management, Cranfield University.
1. The chice of the top 1 percent or the top 5 percent of all returns for construc-
tion of the sample is arbitrary.
2. This chapter is based primarily on the author’s work with Mahesh Pritamani
(2001). This research was among the first to recognize the importance of qual-
ity of information as revealed by large price changes, high trading volumes,
and news. In addition, the chapter relies on work by Park (1995), Cox and
Peterson (1994), Chan (2003), Nofsinger (2001), Fehle and Zdorovtsov (2002),
and Larsen and Madura (2003).
3. Note that a typical week has five trading days. Twenty trading days are ap-
proximately equal to one month.
4. If more analysts are likely to provide updated analysis after good news (so
that their customers can buy those stocks) than after bad news, the effect of
information cascades will be reflected as a larger price drift after positive
surprises than after negative surprises.
5. If the 5 percent cutoff generates too many stocks, the absolute level can be
raised to 7.5 percent. If there are too few stocks, then the level can be lowered
to, say, 2.5 percent.
Beyond the Random Walk78
There is evidence to suggest that industry portfolios exhibit momentum.
Industries that have done well in one period also do well in the next
period. Moreover, industries with no related futures markets are likely
to show greater momentum than industries where information regard-
ing real assets is aggregated in futures prices. Industry portfolios con-
structed in this manner generate returns that may be much larger than
the S&P 500 return.
Investment practitioners believe that asset allocation among bonds,
domestic stocks, and foreign stocks should be altered over time de-
pending on individual circumstances and economic conditions.1
chapter proposes taking asset allocation a step further, to allocation
among different industries. One industry may be hot today and
another may be hot next month depending on changing fads, indi-
vidual preferences, national requirements, or political expediency.
For example, after the terrorist attacks on September 11, 2001, the
defense and security industry did exceptionally well, as demand
for such equipment and personnel increased. Similarly, bad weather
or continued drought can affect production of commodities and hurt
industries that use those inputs.
If changes in an industry are not fleeting but sustained, then a
change in stock prices should mirror changes in the industry. How-
ever, if changes in an industry occur gradually, then stock prices
may also change gradually. Evidence tends to support gradual move-
Momentum in Industry Portfolios 79
ment in industries and in returns of industry portfolios. This means
that compared to an industry that underperforms, an industry that
does well in one period is more likely to do well in the next period.
Such predictability of returns enables the creation and implementa-
tion of profitable trading strategies.
Before presenting evidence related to industry momentum, it is in-
structive to discuss momentum in individual stocks. There is exten-
sive empirical evidence to suggest profitability of trading strategies
based on buying and holding winner stocks. In a typical strategy,
an investor buys a group of stocks that have done well over a speci-
fied period (winner stocks) and short-sells another group of stocks
that have done poorly over the same period (loser stocks). Evidence
suggests that this zero investment strategy generates a positive an-
nual return of up to 12 percent. The strategy doesn’t work for short
periods of less than one month or long periods of more than twenty-
four months, but it has proven to be successful in the six-to-twelve-
month range. Some researchers believe that the momentum is due
to herding by institutional investors, when many institutional in-
vestors buy the same or similar securities. Others believe that irra-
tional individual investor behavior is responsible for the profitability
of momentum strategies.
egies are much less profitable and largely insignificant. This means
that the primary reason for momentum is trends in industry. There-
fore, industry-momentum-based trading strategies are likely to be
better than strategies based on individual stocks without consider-
ing their industry group.
Evidence based on 1963–1995 data supports this conjecture. An
industry-momentum-based trading strategy, where the three best-
performing industries based on one month’s return are bought and
the three worst-performing industries are short-sold, generates an
annualized profit of 12 percent over the following one month. If the
industry effect in the momentum strategy is neutralized, then the
return becomes much smaller.
Although these returns are large and significant, implementing
such a strategy is entirely another matter. There are at least two
Beyond the Random Walk80
limitations. First, strategies involving momentum-based trading of
individual stocks require extensive short selling. Hedged short sales,
as in the case of merger arbitrage, may be acceptable to most inves-
tors, but open, unhedged short positions are generally avoided by
individuals and institutions alike. Therefore, ideally a trading strat-
egy should not contain any speculative short sales. Second, trading
in individual stocks can become expensive. Moreover, trading mul-
tiple stocks within each industry to control risk raises transaction
costs with the consequent decimation of returns.
FIDELITY SECTOR MUTUAL FUNDS
A study of Fidelity sector mutual funds provides more evidence.
Fidelity Select funds are undiversified single-industry mutual funds
designed to capture industry movements with a few stocks. The
advantage of Fidelity Select funds over homemade industry portfo-
lios is that the cost of trading and maintaining a portfolio of Fidelity
Select funds is relatively small. Trading among Fidelity sector funds
can be costless if the portfolio is held for at least thirty days and
traded via the Fidelity website without the assistance of a Fidelity
representative. The short-term trading fee is 0.75 percent if the fund
is held for less than thirty days, and exchanges through a Fidelity
representative cost $7.50.
There are two potential limitations of Fidelity sector funds. First,
these portfolios reflect gains or losses due to active management by
the fund manager. The fund manager will alter the portfolio de-
pending on his perception of the prospects of a particular company.
If the manager is uncertain about the whole industry, he may re-
duce exposure by holding cash, making exposure to the industry
incomplete. Second, the fees and expenses associated with the portfo-
lios can be large. The expense ratio, which includes administrative
costs and management fees, is about 2 percent per year. Addition-
ally, nearly all sector funds have annual turnovers in excess of 100
percent. This means that, on average, all stocks are traded at least
once a year. Such frequent trading will affect returns negatively. The
transaction costs, such as the bid-ask spread and brokerage fees, are
not part of the expense ratio. In spite of these shortcomings, Fidel-
ity sector funds are a superior vehicle for industry-momentum-based
The trading strategy is implemented in the following manner:
the best-performing fund over a six-month period is chosen and
held for the subsequent six-month period. For instance, using data
for the November 1988 to April 1999 period, the first estimation
Momentum in Industry Portfolios 81
period for selection of the best-performing fund is from November
1988 to April 1989, and the first holding period for the identified
fund is from May 1989 to October 1989. The second estimation pe-
riod is from May 1989 to October 1989, and the second holding pe-
riod is from November 1989 to April 1990. There are twenty
nonoverlapping six-month periods over the May 1989–April 1999
period. The aforementioned trading strategy would have generated
an annualized return of 22.4 percent over the ten-year period. In-
stead of using just the single best-performing industry, the risk can
be slightly reduced by holding the top three industries. With three
industries, the annualized return falls to 18.7 percent. Results for
various strategies are summarized in Table 5.1, which shows that
returns improve with longer estimation and longer holding peri-
ods. This result is slightly different from the earlier result, where
industry-momentum strategies are most profitable for one-month
evaluation and one-month holding periods.
Risk becomes important in momentum-based trading strategies
because the portfolio is inadequately diversified—only a few in-
dustries are selected for investment. From Table 5.1, it is apparent
that these strategies are clearly riskier than holding a broader mar-
ket portfolio. A simple and commonly used measure of the risk-
return trade-off is the Sharpe ratio.2
The ratio is calculated as:
Table 5.1 Returns for Trading Strategies with Fidelity Sector Funds, May 1989
to April 1999
Holding Holding Holding Holding
Period: Period: Period: Period
6 Months 12 Months 6 Months 12 Months
Number of 3 6 6 6
6-month 18.7 20.2 20.0 22.7
estimation (25.7) (25.5) (21.2) (22.1)
12-month 22.2 26.5 20.5 22.1
estimation (23.9) (24.6) (21.3) (22.1)
S&P 500 return 18.7 18.7 18.7 18.7
(%) (15.7) (15.7) (15.7) (15.7)
Wilshire 5000 17.7 17.7 17.7 17.7
(%) (15.8) (15.8) (15.8) (15.8)
Russell 2000 12.0 12.0 12.0 12.0
(%) (19.1) (19.1) (19.1) (19.1)
All returns are annualized, and the standard deviations of returns are in parentheses. This
table is derived from O’Neal (2000).
Beyond the Random Walk82
Portfolio return – Return on Treasury bills
Standard deviation of portfolio return
The Sharpe ratios are reported below based on the average short-
term interest rate and annual returns for two trading strategies and
three indexes over the May 1989–April 1999 period.
6-month estimation period,
12-month holding, 3 industries 0.58
12-month estimation period,
12-month holding, 3 industries 0.86
S&P 500 holding return 0.86
Wilshire 5000 holding return 0.78
Russell 2000 holding return 0.35
Sector fund trading strategies do not outperform the S&P 500 af-
ter accounting for risk. However, the trading strategies are gener-
ally superior when compared with other mutual funds, and other
indexes. If only the beta risk (or systematic risk) is considered (as-
suming the sector funds are held in an otherwise well-diversified
portfolio), the sector fund trading strategies are superior, in gen-
eral, to almost all other mutual funds, including the S&P 500 index
funds. All of the data presented in this section for Fidelity sector
funds are based on long holding periods. Later in this chapter we
will see that Fidelity sector funds perform quite well over shorter
holding periods. Those results are similar to the results reported
earlier in this section.
The momentum in individual stock returns and industry returns
suggests underreaction to new information that may be inconsis-
tent with market efficiency. What can explain the observed momen-
tum in industry portfolios? There are two broad categories of
explanations: one is based on irrational investor behavior, and the
other is based on efficient markets.
Behavioral finance theories (see Chapter 12) attribute under-
reaction and overreaction to investor irrationality. According to this
explanation, investors are reluctant to change their beliefs quickly
even in the face of convincing new information. As a result, they
Momentum in Industry Portfolios 83
underreact, giving rise to momentum. Smart investors may be un-
able to take advantage of these biases because their actions are of-
ten limited by capital availability and uncertainty. For example, the
exploding Internet valuations in 1999 and 2000 could not be con-
trolled despite strong beliefs among smart investors that these were
Another explanation is related to lags in revisions by analysts.
Firms that are industry leaders are followed by many stock ana-
lysts, while smaller firms in the same industry are followed by fewer
analysts. The extent of coverage affects the frequency with which
those stocks are reviewed. Leader stocks tend to get reviewed early,
with dissemination of new information and the consequent price
impact. Other industry stocks are reviewed later but experience a
similar price impact. The lead-lag relationship in information dis-
semination can result in the observed momentum.
Besides the behavior of irrational individual investors, institu-
tional managers can be responsible for momentum. It is always less
risky for a manager to go with the crowd than to stick his neck out.
Therefore, when a few institutional managers begin to buy a par-
ticular stock, other managers may feel safe in buying the same stock,
resulting in momentum. This is popularly known as herding.
Finally, a rational explanation that is consistent with momentum
arises from the relationship between financial markets and real as-
sets. While financial asset prices can reflect all available informa-
tion, prices of real goods are known to be sticky. Prices of real goods,
such as food and housing, move slowly because the demand for
these products changes slowly. Since financial markets reflect ex-
pectations related to markets for real goods, financial asset prices
also move slowly. One can rightly claim that financial markets should
be able to forecast industry profitability depending on forecasts of
supply and demand. The problem is that financial markets that can
aggregate information related to forecasts of futures prices do not
exist for all industries. Consider the semiconductor industry. An
analyst can forecast semiconductor prices for the next few months.
However, that forecast represents a single data point and may not
reflect the market wisdom. Many well-informed market participants
may choose not to participate or may be ignored by market ana-
lysts. If futures prices did exist for the semiconductor industry, as
they do for crude oil on the New York Mercantile Exchange, the
semiconductor futures prices would more accurately reflect an ag-
gregation of market information. For industries with futures prices,
the forecasts are much easier and more accurate, and there may be a
smaller momentum effect.
Beyond the Random Walk84
To illustrate momentum in an industry where futures prices are
not available, consider the demand for security and defense equip-
ment after September 11, 2001. The stock prices of security equip-
ment providers rose immediately on anticipation of increased
demand. However, no one knew exactly how much the demand
would rise. The companies themselves were in the dark. Corporate
estimates were based on actual sales rather than anticipated sales.
As the orders for security and defense equipment kept pouring in,
first from U.S. agencies and then from foreign government agen-
cies, the demand estimates were continually revised upward. Con-
sequently, the stock prices continued to rise. The returns to Fidelity’s
sector fund for the defense industry (ticker: FSDAX) are given be-
low along with the S&P 500 return for comparison:
Month FSDAX Return (%) S&P 500 Return (%)
October 2001 3.6 1.9
November 2001 3.8 7.7
December 2001 4.1 0.9
January 2002 5.8 –1.6
February 2002 2.3 –1.9
March 2002 4.6 3.8
April 2002 2.0 –6.1
May 2002 0.7 –0.7
June 2002 –3.0 –7.1
The FSDAX return is positive for eight out of nine months follow-
ing the attacks, and becomes negative only in the last month. Com-
pared to the S&P 500 return, the return for the defense industry is
also larger in eight out of nine months. Overall, the defense sector
earned a return of 23.9 percent versus a return of –3.0 percent for
the S&P 500 over the nine-month period.
Why couldn’t the increase in demand be anticipated more accu-
rately? On average, the demand forecasts should equal the actual
demand. The main reason may be the absence of financial markets
that aggregate available information. Futures markets for commodi-
ties such as crude oil, orange juice, lumber, hogs, chicken, coffee,
cotton, and so on aggregate all publicly available information. No
such mechanism or financial market exists for futures prices of se-
curity and defense equipment. The primary sources of information
are corporate officers and financial analysts, who tend to be conser-
vative in revising estimates, possibly contributing to the momen-
tum in stock prices.
Momentum in Industry Portfolios 85
Given the evidence related to industry momentum, a natural ques-
tion that follows is: Why does it still persist? There may be several
reasons. First, there is a fair amount of skepticism relating to mo-
mentum in spite of the evidence. More work is needed to convince
investors that individual stock momentum or industry momentum
exists. Once that happens, investors may feel more confident about
taking positions to arbitrage and eventually eliminate momentum.
Second, no clear explanations have emerged to explain momentum.
Besides failing to convince the ordinary investor, behavioral expla-
nations introduce greater risk and uncertainty because investor be-
havior can change without warning. Lack of an adequate explanation
increases the skepticism with the results. Third, the evidence re-
lated to individual stock momentum not attributable to industries
is strongest at periods of intermediate length (six to twelve months).
Whenever mispricings occur at intervals in excess of about one
month, estimation of risk and computation of abnormal returns can
become important. The evidence indicates that industry based mo-
mentum is also strong at short intervals of about one month. There-
fore, misestimation of abnormal return becomes less of an issue with
industry-based momentum. However, the skepticism of industry
momentum mentioned above becomes more critical because the
evidence of industry-based momentum is new.
Trading Process and
IMPLEMENTATION WITH MANY MUTUAL FUNDS
Evidence supporting the existence of industry momentum presented
in the “Explanations” section is limited to reliance on individual
stocks and Fidelity’s sector funds. While the use of mutual funds is
preferred to individual stocks, there is no need to restrict the choice
to Fidelity funds alone. Many other fund families, such as Rydex,
ProFunds, Icon, and Invesco, offer sector funds. A combination of
mutual funds for a particular industry from different fund families
is likely to reduce manager-specific risk and probably more fully
span the industry than a single sector fund. It is worth exploring
the profitability of trading strategies based on a larger sample of
Beyond the Random Walk86
The construction of the mutual fund sample and results are de-
scribed below. The period analyzed here is January 1997 to Decem-
ber 2001. In the next section, the same strategy is employed for the
first half of 2002.
Step 1: The first step is to identify and choose broad industries.
Fidelity’s forty-one sector funds are a good starting point. How-
ever, each fund need not represent a distinct industry. Some of the
Fidelity funds belong to the same industry and even have consider-
able overlap. For example, Select Computers and Select Software
and Computers can be merged into a single industry. In order to
have sufficient historical data, only funds that were established be-
fore 1997 are considered. The assignment of the forty-one Fidelity
funds into distinct industries is shown in Table 5.2. The final sample
consists of twenty-four industries.
Step 2: In addition to the Fidelity funds, pick other sector mutual
funds that fit into the twenty-four industries, irrespective of the fund
family. These other funds come from Morningstar’s Principia Pro,
which has a fairly broad coverage of mutual funds. Sector funds are
usually, but not always, categorized by Morningstar under “Spe-
cialty.” Therefore, besides identifying funds from the “Specialty”
category, it is desirable to peruse all funds offered by Fidelity, Rydex,
Invesco, ProFunds, and Icon individually.
Step 3: To make the sample of mutual funds accessible to most
investors, several screens are imposed for selection. First, the mini-
mum purchase amount must not exceed $25,000. Actually, the mini-
mum amount is typically $1,000 to $5,000. Only Rydex has a
minimum amount of $25,000. Second, only one fund is chosen when
funds with multiple classes are offered. The selection process is bi-
ased toward using funds with zero or low loads and funds with a
high asset base. After these screens, up to the top five funds in each
industry by assets are selected. The funds are listed by ticker sym-
bols in Table 5.3.
Step 4: The next step is to obtain historical prices, including dis-
tributions, for the funds selected in the previous step. The weekly
return is computed as the return from Wednesday close to the next
Wednesday close. If Wednesday is a nontrading day, then the next
business day’s close is considered. You can compound five weekly
returns to get a five-week return that is a close approximation to the
Step 5: To select funds for the trading strategy, calculate the peri-
odic return (either weekly or for periods of five weeks) for each sec-
tor. Then calculate the mean overall return for twenty-four industries.
Table 5.2 Fidelity Sector Funds and Industry Categories
Inception Industry Reason for
Name Ticker Date Assignment Nonassignment
1. Fidelity Select Air Transportation FSAIX Dec. 1985 Airlines
2. Fidelity Select Automotive FSAVX Jun. 1986 Transportation
3. Fidelity Select Banking FSRBX Jun. 1986 Banking
4. Fidelity Select Biotechnology FBIOX Dec. 1985 Biotechnology
5. Fidelity Select Brokerage and FSLBX Jul. 1985 Banking
6. Fidelity Select Business Services FBSOX Feb. 1998 No assignment Sector is too new
7. Fidelity Select Chemicals FSCHX Jul. 1985 Basic materials
8. Fidelity Select Computers FDCPX Jul. 1985 Computers
9. Fidelity Select Construction and Housing FSHOX Sep. 1986 Real estate
10. Fidelity Select Consumer Industries FSCPX Jun. 1990 Consumer
11. Fidelity Select Cyclical Industries FCYIX Mar. 1997 No assignment Sector is too new
12. Fidelity Select Defense and Aerospace FSDAX May 1984 Defense
13. Fidelity Select Developing FSDCX Jun. 1990 Communications
14. Fidelity Select Electronics FSELX Jul. 1985 Electronics
15. Fidelity Select Energy FSENX Jul. 1981 Energy
16. Fidelity Select Energy Services FSESX Dec. 1985 Energy services
17. Fidelity Select Environmental FSLEX Jun. 1989 No assignment Sector is too narrow
18. Fidelity Select Financial Services FIDSX Dec. 1981 Financial services
19. Fidelity Select Food and Agriculture FDFAX Jul. 1985 Food
20. Fidelity Select Gold FSAGX Dec. 1985 Gold
21. Fidelity Select Health Care FSPHX Jul. 1981 Health care
22. Fidelity Select Home Finance FSVLX Dec. 1985 Banking
(continues on next page)
Table 5.2 Fidelity Sector Funds and Industry Categories (continued )
Inception Industry Reason for
Name Ticker Date Assignment Nonassignment
23. Fidelity Select Industrial Equipment FSCGX Sep. 1986 Industrials
24. Fidelity Select Industrial Materials FSDPX Sep. 1986 Basic materials
25. Fidelity Select Insurance FSPCX Dec. 1985 Financial services
26. Fidelity Select Leisure FDLSX May 1984 Leisure
27. Fidelity Select Medical Delivery FSHCX Jun. 1986 Health care
28. Fidelity Select Medical Equipment FSMEX Apr. 1998 Health care
29. Fidelity Select Multimedia FBMPX Jun. 1986 Communications
30. Fidelity Select Natural Gas FSNGX Apr. 1993 Energy
31. Fidelity Select Natural Resources FNARX Mar. 1997 Natural resources
32. Fidelity Select Networking and FNINX Sep. 2000 No assignment Sector is too new
33. Fidelity Select Paper and Forest Products FSPFX Jun. 1986 Natural resources
34. Fidelity Select Pharmaceuticals FPHAX Jun. 2001 Health care
35. Fidelity Select Retailing FSRPX Dec. 1985 Retailing
36. Fidelity Select Software and Computer FSCSX Jul. 1985 Computers
37. Fidelity Select Technology FSPTX Jul. 1981 Technology
38. Fidelity Select Telecommunications FSTCX Jul. 1985 Telecommunications
39. Fidelity Select Transportation FSRFX Sep. 1996 Transportation
40. Fidelity Select Utilities Growth FSUTX Dec. 1981 Utilities
41. Fidelity Select Wireless FWRLX Sep. 2000 No assignment Sector is too new
Momentum in Industry Portfolios 89
Step 6: A very simple trading strategy is implemented. Usually,
the simplest strategies are the most effective and longest-lasting.
The strategy is to choose sectors whose return exceeds the mean
return for all industries. Invest in these sectors over the next period.
The results are reported in Table 5.4.
Two different holding periods, one-week and five-week, are con-
sidered for the rest of the chapter. The choice of these holding peri-
ods is primarily for convenience. Longer holding periods are not
considered for two reasons. First, the study discussed in “Fidelity
Sector Mutual Funds,” earlier in this chapter, is already based on
longer holding periods, and there is no reason to duplicate those
results. Second, results with longer holding periods do not gener-
ate enough observations, making statistical testing ineffective.
Eventually, the recommendation is to use a five-week holding pe-
riod only. However, for the time being, both one-week and five-
week holding periods are considered.
For each of the two holding periods, three different estimation
periods are used, ranging from one week to twenty-five weeks. An
Table 5.3 Sectors and Sector Funds Used in Analysis
Sector Name Ticker Symbols
1. Airlines FSAIX
2. Banking FSRBX, FSLBX, FSVLX, FRBCX, RYKIX
3 Basic Materials FSCHX, ICBMX, FSDPX, RYBIX, BMPIX
4. Biotechnology FBIOX, FBDIX, DRBNX, RYOIX, ORHBX
5 Communications FSDCX, TCFQX, FBMPX, FTICX, FCTYX
6. Computers FDCPX, FSCSX
7. Consumer ICCCX, RYCAX, FSCPX
8. Defense FSDAX
9. Electronics FSELX, RYSIX, FELCX, SMPIX
10. Energy VGENX, FSTEX, FSENX, FSNGX, UMESX
11. Energy Services FSESX, RYVIX
12. Financial Services FSPCX, FSFSX, FIDSX, PRISX, PBTAX
13. Food FDFAX
14. Gold VGPMX, FSAGX, INIVX, SCGDX, USAGX
15. Health Care VGHCX, FSPHX, FHLSX, SCHLX, FSMEX
16. Industrials ICTRX, FSCGX
17. Leisure FLISX, FDLSX, ICLEX, RYLIX
18. Natural Resources PNRBX, FRNRX, BGRIX, MBGRX, PRGNX
19. Real Estate CSRSX, VGSIX, RRESX, CREEX
20. Retailing FSRPX, RYRIX
21. Technology TVFQX, PRSCX, FSPTX, JAGTX, FTCHX
22. Telecommunication ISWCX, PRMTX, FSTCX, FWRLX, ATINX
23. Transport FSRFX, FSAVX, RYPIX
24. Utilities VGSUX, IUTBX, EVTMX, MMUCX, FSUTX
Table 5.4 Returns to Industry-Momentum-Based Trading Strategies (1997–2001)
Mean Annualized Return to
Return to Return to Success Sectors
Estimation Holding Sectors Held Sectors Held Ratio Not Held Number of
Period Period (%) (%) (%) (%) Observations
Panel A: Sectors with above-average return held for 5 weeks
5 weeks 5 weeks 1.9* 21.6 (23.2) 61 0.7 51
15 weeks 5 weeks 2.2** 25.4 (24.8) 67 0.6 49
25 weeks 5 weeks 2.4** 28.0 (26.4) 66 0.1 47
Panel B: Sectors with above-average return held for 1 week
1 week 1 week 0.37** 21.2 (19.5) 60 0.14 259
3 weeks 1 week 0.39** 22.4 (19.5) 59 0.07 257
5 weeks 1 week 0.41** 23.7 (18.7) 58 0.06 255
Panel C: Sectors with above- average and positive return held for 5 weeks
5 weeks 5 weeks 1.9* 21.6 (23.5) 57 0.7 49
15 weeks 5 weeks 2.2** 25.4 (24.8) 63 0.6 49
25 weeks 5 weeks 2.2* 25.4 (25.5) 66 0.1 47
Panel D: Sectors with above-average and positive return held for 1 week
1 week 1 week 0.35* 19.9 (21.6) 59 0.14 250
3 weeks 1 week 0.39** 22.4 (19.5) 57 0.07 249
5 weeks 1 week 0.42** 24.4 (18.7) 56 0.06 248
S&P 500 annualized return 13.0 (18.2)
The number of observations corresponds to the periods for which funds are held. When estimation period returns must be positive, as in panels C and D, no
positions are taken in a few cases. In those instances, the number of observations is smaller. Standard deviation is in parentheses for the annualized return. **
implies significance at the 5 percent level, and * implies significance at the 10 percent level.
Momentum in Industry Portfolios 91
estimation period is the prior period over which actual returns are
measured to categorize the sectors as underperforming or
overperforming sector. The holding period is the subsequent pe-
riod during which the trading strategy is implemented by invest-
ing in only the overperforming sectors.
Results for a holding period of five weeks are reported in panels
A and C of Table 5.4. The estimation periods for portfolio formation
are five weeks, fifteen weeks, and twenty-five weeks. Funds in in-
dustries that exceed the mean return during the estimation period
are held for a subsequent five-week period. The return for the five-
week holding period with a five-week estimation period is 1.9 per-
cent, or 21.6 percent annualized, significantly greater than zero in a
statistical and economic sense. The return is positive 61 percent of
the time. At the same time, funds in industries that earned below
the mean return in the preceding period earned only 0.7 percent, in
the holding period, which is statistically not different from zero.
During the same 1997–2001 period, the S&P 500’s return was a sta-
tistically insignificant 1.2 percent.
Table 5.4 shows that returns and success ratios are generally higher
for very long estimation periods. This means that the past twenty-
five weeks’ return is a better predictor of the next period’s return
than the past five weeks’ return. In addition, the return to sectors
not held decreases as the estimation period increases, implying the
superiority of the longer estimation period. On the other hand, the
results are not very different across different holding and estima-
In panel B, returns are reported for a one-week holding period
based on one-week, three-week, and five-week estimation periods.
The one-week holding period returns are almost as good as the five-
week holding period annualized returns. There is no improvement
in the success ratio as the estimation period is increased, though
there is an improvement in return. In panels C and D, a slightly
different selection process is used for choosing the sectors to be held.
Instead of holding all sectors with a return above the mean in the
estimation period, an additional condition is imposed: the return of
the sector must be positive. However, the results reveal that neither
the return nor the success ratios are higher with this additional con-
dition than the results in panels A and B without the added screen.
Accordingly, all future analysis is presented based on the simple
strategy of holding sectors above the mean return.
Until now, the risk level of the positions was ignored. However,
it is important to take risk into account because industry-momen-
tum-based trading strategies are clearly riskier than holding a
Beyond the Random Walk92
broader market portfolio. The Sharpe ratio is used to compare the
Sharpe ratios are reported below based on
annual returns for the best-case scenarios, an average return of 4
percent for short-term Treasury bills during 1997–2001, and stan-
dard deviations (reported in parentheses) in Table 5.4.
25-week estimation period and 5-week holding period 0.91
5-week estimation period and 5-week holding period 0.76
5-week estimation period and 1-week holding period 1.05
S&P 500 holding return 0.49
Since higher Sharpe ratios indicate superior investment, the best
results are for the one-week holding period, with a ratio of 1.05. The
five-week holding period with a twenty-five-week estimation pe-
riod is only slightly lower at 0.91. Moreover, once short-term re-
demption fees are considered, it may be desirable to hold the sectors
for five weeks rather than just one week. In any case, all three in-
dustry-momentum-based trading strategies have a significantly
better Sharpe ratio than a buy-and-hold S&P 500 strategy, which
has a Sharpe ratio of only 0.49.
The difference in returns between sectors held and sectors not
held is reassuring because it suggests that superior performance of
sectors held is unlikely to be accidental.
IMPLEMENTATION FOR INDUSTRIES WITH AND
WITHOUT FUTURES MARKETS
It is possible to improve returns from an industry-momentum-based
trading strategy by relying on the rational explanation that indus-
try momentum probably exists for industries that do not have fu-
tures markets (see “Explanations” above). Futures markets, like other
financial markets, are aggregators of information. Since commod-
ity futures prices capture information about trends in commodity
prices, participants in financial markets can make better-informed
decisions in industries dependent on commodities with traded fu-
tures markets than in industries without futures markets.
If the futures markets’ explanation is indeed true, then industries
with futures markets will exhibit much less momentum than in-
dustries without futures markets. And selecting only industries
without futures markets will sharpen and strengthen the gains due
to industry momentum.
Of the industries listed in Table 5.3, commodity futures represent
a significant part of the following industries:
Momentum in Industry Portfolios 93
• Gold. Futures exist for gold, silver, copper, platinum, and pal-
• Energy. Futures exist for crude oil, heating oil, propane gas,
and natural gas.
• Energy services. This demand is derived from energy prices.
• Airlines. Fuel constitutes a large portion of airline costs.
• Natural resources. Futures exist for oil, gas, and lumber.
• Food. Futures exist for corn, wheat, soybeans, coffee, orange
juice, and sugar.
Sectors are divided into two groups: one where futures markets
exist (the six industries) and the other where futures markets do not
exist (the remaining seventeen industries). Industry-momentum-
based strategies are constructed separately for the two groups but
in a manner similar to that for Table 5.4.
The results are in Table 5.5. Three points need emphasis. First, in
sectors with futures markets, there is no evidence of any industry
momentum. Whether well-performing sectors are held or poorly
performing sectors are held, the returns for the five-week holding
period are in the 0.70–0.85 percent range. There is no perceptible
difference between the well-performing and poorly performing
subsamples. On the other hand, there is clear and strong evidence
of industry momentum in sectors without futures markets. Well-
performing sectors in the estimation period outperform the other
sectors during the holding period. The results for the one-week hold-
ing period are similar to those for the five-week holding period.
The obvious implication is that industry momentum occurs only
for sectors where futures markets do not exist. Finally, the results
based on sectors without futures markets are somewhat stronger
than the results in Table 5.4. Therefore, it is preferable to concen-
trate only on sectors without futures markets when constructing
trading strategies based on industry momentum. Accordingly, trad-
ing strategies in the remainder of this chapter are constructed on
the basis of industries that do not have futures markets.
IMPLEMENTATION WITH FIDELITY AND RYDEX FUNDS
The results in the previous sections are based on a large number of
funds. While the large number is useful in spanning the entire in-
dustry and minimizing the risk of any one industry, many funds
are inconvenient and costly to trade. For example, if about one-half
Table 5.5. Returns to Industries with and without Futures Markets (1997–2001)
Sectors without Futures Markets Sectors with Futures Markets
Sectors with Sectors with Sectors with Sectors with
above-average below-average above-average below-average
return in return in return in return in
Estimation Holding prior period prior period prior period prior period Number of
Period Period (%) (%) (%) (%) Observations
5 weeks 5 weeks 2.32** 0.44 0.80 0.72 51
15 weeks 5 weeks 2.60** 0.42 0.78 0.84 49
25 weeks 5 weeks 2.82** 0.10 0.76 0.71 47
S&P 500 return 5 weeks 1.18 1.18 1.18 1.18 52
1 week 1 week 0.41** 0.18 0.31 0.06 259
3 weeks 1 week 0.49** 0.08 0.21 0.12 257
5 weeks 1 week 0.47** 0.08 0.21 0.14 255
S&P 500 return 1 week 0.23 0.23 0.23 0.23 260
Futures markets exist for the following industries: gold, natural resources, energy, energy services (derived demand from energy), food, and airlines (profitability
depends on oil prices). ** implies significance at the 5 percent level. None of the returns in columns 4, 5, and 6 is significantly different from zero.
Momentum in Industry Portfolios 95
of the sectors are above the mean return, it implies that one would
have to trade forty to fifty funds of five or six different mutual fund
companies. While that is practical for large investors, it is not desir-
able for small investors. Therefore, it is worthwhile to explore
whether intrafamily fund transfers are possible while earning rea-
The two firms with the largest number of sector funds, Fidelity
and Rydex, are selected for this experiment. Although Fidelity has
forty-one sector funds in twenty-four industries, only thirty-five
funds in twenty-four industries that were in existence in January
1997 are considered. Rydex has seventeen funds spanning sixteen
industries. Of these, only fifteen Rydex funds covering fifteen in-
dustries are chosen, all of which were created in April 1998.
As mentioned above, Fidelity allows costless exchanges through
their website provided the sector fund is held for at least thirty days.
Fidelity does have an initial sales load of 3 percent, but that load
has to be paid just once. Fidelity usually waives the sales load for
401(k) and retirement accounts. Rydex allows exchanges among its
various funds with no fees or constraints. Rydex funds are no-load
funds, but entry into the Rydex family of funds requires a mini-
mum initial investment of $25,000.4
The results of trading Rydex funds and Fidelity funds within each
family are reported in Table 5.6. Fidelity sector funds perform at least
as well as the universe of funds considered in Table 5.5. The twenty-
five-week estimation period and five-week holding period returns
are 2.82 percent for the sample of all funds in Table 5.5 but slightly
higher at 2.94 percent for Fidelity funds. The one-week holding pe-
riod returns for Fidelity funds and All funds are almost identical.
The performance of Rydex funds is not as good except for the
twenty-five-week estimation period and five-week holding period
strategy. However, the difference in returns could be attributed to
different observation periods. The five-week S&P 500 return for the
April 1998–December 2001 period is 0.54 percent, compared with
1.11 percent for the 1997–2001 period. If the abnormal return for
Rydex funds is considered, it can be seen that performance of Rydex
funds is comparable to that obtained for Fidelity funds. However,
Fidelity funds are preferred because they cover more industries.
IMPLEMENTATION IN REAL TIME
The above strategy is implemented in real time for the January 2002–
June 2002 period. The industry-momentum-based trading strategy
that is adopted here consists of the following steps:
Table 5.6 Industry Momentum Returns for Rydex and Fidelity Funds
Fidelity Funds: 1997–2001 Rydex Funds: April 1998–2001
Sectors with Sectors with
Return in Success Return in Success
Estimation Holding Prior Period Ratio Number of Prior Period Ratio Number of
Period Period (%) (%) Observations (%) (%) Observations
5 weeks 5 weeks 2.31** 61 51 1.89 57 33
15 weeks 5 weeks 2.62** 59 49 1.88 58 31
25 weeks 5 weeks 2.94** 68 47 3.09* 66 29
S&P 500 return 5 weeks 1.11 N.A. 0.54 N.A.
1 week 1 week 0.42** 60 259 0.30 57 171
3 weeks 1 week 0.49** 60 257 0.29 55 169
5 weeks 1 week 0.47** 59 255 0.40 56 167
S&P 500 return 1 week 0.21 N.A. 260 0.15 N.A. 172
Only sectors without futures markets. Rydex funds in existence as of April 1998 and Fidelity funds in existence as of January 1997. ** implies significance at the
5% level, and * implies significance at the 10% level.
Momentum in Industry Portfolios 97
• Select funds in each of the seventeen industries that do not
have futures markets. If only Rydex or Fidelity sector funds
are used, then those funds may not span all of the seventeen
• Estimate the return over the estimation period. Funds that earn
an above-average return are held during the holding period. The
holding period must be at least thirty days for Fidelity funds.
• Repeat the previous step upon completion of the holding period.
The results are in Table 5.7. The stock market performed poorly
during the January-June 2002 period. The trading strategies based
on industry momentum convincingly outperformed the S&P 500;
though in most cases the raw returns are negative, they are usually
much less negative than the S&P 500. Using the sample of All funds
generates a return of –1.5 percent for a five-week holding period
with a twenty-five-week estimation period, and a return of –3.9
percent for a one-week holding period with a five-week estimation
period. These returns are significantly superior to the S&P 500 re-
turns of –8.8 percent and –15.9 percent, respectively. The Fidelity
returns are similar to the returns for All funds, and occasionally
better. However, the Rydex funds do not perform as well. They have
Table 5.7 Industry Momentum Returns for the January–June 2002 Period
Sectors with Above-Average
Return in Prior Period
All Fidelity Rydex
Estimation Holding Funds Funds Funds
Period Period (%) (%) (%)
There are five 5-week holding periods beginning on December 5, 2001, and
ending on May 29, 2002. Total return for those periods is reported below.
5 weeks 5 weeks 2.2 3.5 –0.1
15 weeks 5 weeks –3.8 –0.5 –6.1
25 weeks 5 weeks –1.5 –2.5 –8.1
S&P 500 return 5 weeks –8.8 –8.8 –8.8
There are twenty-six 1-week holding periods beginning on December 26, 2001,
and ending on June 26, 2002. Total return for those periods is reported below.
1 week 1 week –16.6 –15.3 –24.6
3 weeks 1 week –13.5 –10.0 –16.8
5 weeks 1 week –3.9 –3.9 –7.8
S&P 500 return 1 week –15.9 –15.9 –15.9
Only sectors without futures markets are evaluated. Rydex funds in existence as of April 1998
and Fidelity funds in existence as of January 1997 are considered.
Beyond the Random Walk98
lower returns than Fidelity and the sample of All funds for all esti-
mation and holding periods. The use of Fidelity funds continues to
be the preferred mode of capturing industry momentum.
Overall, one can see that investing in sector funds that have done
well in the prior period is a superior strategy compared to holding
the broader market. As shown in this section, it is also a simple
strategy to implement.
IMPLEMENTATION THROUGH SECTOR FUND NEWSLETTERS
As an alternative to designing the strategy, you can rely on sector
fund newsletters. Sector fund switching is particularly popular in
the newsletters. The newsletters will suggest when to switch into
which industry, or how to “play the sector game.” A word of cau-
tion is in order, however, as newsletters suffer from severe survi-
vorship biases (see Chapter 1). To show a string of good results, the
newsletters routinely abandon old, unprofitable strategies, create
new ones based on past data that seem to work for some time, and
then discard them once they cease to perform. Hulbert’s Financial
Digest (HFD) provides some guidance by tracking the performance
of newsletters and their strategies. It rates the timing newsletters
based on the actual return that could have been earned based on
the recommendations. However, HFD also suffers from a survivor-
ship bias, though less severe—only newsletters’ portfolios that have
continued to do well will be retained by the newsletters and, there-
fore, only the winning portfolios, by luck or design, will get cov-
ered by HFD.
The sector newsletters covered by HFD as of June 2002 are listed
in “Sector Fund Newsletters” later in this chapter. Each newsletter
offers many different portfolios and many different combinations
that can often be confusing. Whether you should use a newsletter is
a difficult question to answer. On one hand, newsletters use sophis-
ticated technical analysis for making recommendations that may be
superior to the simple strategy described herein.Also, it is a lot easier
to pay a newsletter to make recommendations than to compute the
returns every month. On the other hand, sophisticated technical
analysis, which is usually devoid of economic content, may not be
much better than data mining. If you decide to choose a newsletter,
make sure it has at least a five-year record. Also, try to understand
the system to determine whether it is following the strategies out-
lined and tested here. It is even more important to feel comfortable
and trust the newsletter. You want to find one that is honest, dis-
closes limitations of the strategy other than as a disclaimer, and does
Momentum in Industry Portfolios 99
not constantly keep changing the rules. It is best to try out the news-
letter for about six months before actually implementing its sector
IMPLEMENTATION WITH RYDEX’S SECTOR ROTATION FUND
In addition to the newsletters, there is one sector rotation fund that
explicitly tries to buy hot sectors and sell cold sectors. The Rydex
Sector Rotation Fund (RYISX) debuted in March 2002. It ranks fifty-
nine industries and picks the best-performing ones for investment.
The fund is not based on the principles discussed in this chapter. It
also invests in individual stocks and short-sells as necessary. Since
the fund is new, it is difficult to evaluate its performance. However,
so far its performance has not been particularly encouraging.
The evidence and trading strategy recommendations presented in
this chapter rely on past data. Since future market conditions and
market patterns may be completely different, there is no certainty
Trading Based on Industry Momentum
S&P 500 Return
Sectors with above-
Sectors with below-
Figure 5.1 The figure shows the S&P 500 buy-and-hold return compared with the
returns for above average and below average sectors based on five-week and fif-
teen-week estimation periods. The data are from 1997–2001 and represent a five-
week holding period.
Beyond the Random Walk100
industry momentum will continue in the future or be profitable.
Trading strategies based on momentum are particularly risky be-
cause only a few industries are held, resulting in inadequate diver-
• Research has discovered that stocks exhibit momentum. Stocks
that have done well in one period are more likely to do well in
the following period. Momentum among stocks is particularly
high for intermediate holding periods ranging from about six
to twelve months.
• Momentum among stocks seems to arise from industry momen-
tum. If an industry is doing well, then it tends to continue to do
well. Industry momentum occurs at short intervals (periods of
one month) and at intermediate intervals of six to twelve months.
• Sector mutual funds can be used to study or benefit from in-
dustry momentum. Analysis of Fidelity sector funds reveals
that higher returns, albeit with higher risk, can be earned by
following an industry-momentum-based trading strategy.
• Irrational investor behavior can explain momentum, as inves-
tors often either chase winning stocks or underreact to new
information. However, industry momentum may also occur
because there is no mechanism to aggregate information about
future prices of real goods. In the absence of this information,
financial markets rely on companies and analysts who are slow
in updating earnings forecasts.
• The evidence presented shows that industry momentum is
profitable. The Sharpe ratio of returns for momentum strate-
gies is almost twice as large as that for the S&P 500.
• Atest of the explanation related to futures markets reveals that
industry momentum is more profitable when only industries
without futures markets are traded.
• Among fund families that offer sector funds, Fidelity is supe-
rior and as good as holding multiple funds in the same indus-
try. Rydex funds, on the other hand, do not perform as well.
Another possibility not considered explicitly in the book is the
use of S&P sector exchange-traded funds.
Momentum in Industry Portfolios 101
• A trading strategy is employed for the January-June 2002 pe-
riod. The strategy generates a negative return of –1.5 percent.
However, this return is much better than the –8.8 percent earned
by the S&P 500 over the same period.
• Numerous advisory services are available for timing indus-
trial sectors, especially with Fidelity funds. According to Hul-
bert’s Financial Digest, some of these services have a good record
of outperforming the market.
Momentum within an industry suggests that investors can actually
chase winning sectors and profit from them. Fidelity sector funds offer
an easy way to switch among different “hot” sectors. Industry funds
that outperform the average industry fund over a six-month period
are likely to generate annual abnormal returns of more than 10 per-
cent. The Sharpe ratio, which accounts for risk, is much higher for an
industry-momentum-based trading strategy than for the S&P 500.
Historical Mutual Fund Price Data
http://www.qp2.com: Quotes-Plus has about fifteen thousand mutual funds in
its database and provides about ten years of historical price data.
http://www.morningstar.com: For data about specialty funds and other
Fund Families with Sector Funds
http://www.fidelity.com: Go to “Mutual Funds,” then to “Learn About Fidelity
Funds,” followed by “Browse Our Funds,” and finally to “Fidelity’s Select
http://www.rydexfunds.com: The Rydex website.
http://www.invesco.com, http://www.profunds.com, and
http://www.iconfunds.com: Other fund families.
Sector Fund Newsletters
http://www.allstarinvestor.com: Offers switching advice on Fidelity single-
sector portfolio, Fidelity’s multisector portfolio, Rydex funds, and ProFunds.
Followed by Hulbert’s Financial Digest since December 31, 1992. HFD ranks
its single-sector portfolio as one of the top-performing portfolios.
http://www.soundsectorstrategy.com: Offers switching advice on Rydex funds
and ProFunds, and various levels of service, including free service. Followed
by HFD since December 31, 2000. Underperformed the market.
Beyond the Random Walk102
http://www.fabian.com: Look for “Sector Advising” near the top right corner.
Followed by HFD since April 30, 2002, for switching advice on Rydex and
exchange-traded funds, and since December 31, 1998, for Fidelity and Rydex
http://www.fidelitymonitor.com: Relatively inexpensive and has performed
well. Concentrates on the Fidelity sector portfolio. HFD has followed the
Fidelity Select system of this newsletter since December 31, 1986.
http://www.fidelityinvestor.com: Quite expensive but has performed well.
Concentrates on the Fidelity sector portfolio. HFD has followed the Fidelity
sector investor portfolio of this newsletter since December 31, 1999.
http://www.kenjolfr.com/: Alphatimer strategy at this site offers a portfolio of
Rydex sector funds and another portfolio of Fidelity funds. The Fidelity
Alpha and Rydex Alpha sectors have performed well. HFD has followed the
recommendations since December 31, 1999.
http://www.stockmarketcycles.com: Offers advice on Fidelity select switchers
and on Rydex switchers. Reasonable performance with Fidelity. Followed by
HFD since December 31, 1984.
http://www.timing.net: Performance is questionable. Followed by HFD since
December 31, 1998.
http://www.selectinvestor.com: The newsletter recommends four portfolios
based on Fidelity’s sector funds. Reasonable performer, but each of the four
portfolios may be too narrow. Followed by HFD since December 31, 1999.
http://www.timerdigest.com: Concentrates on the Fidelity select program.
Good performer. Followed by HFD since December 31, 1987.
References for Further Reading
Dellva, Wilfred L., Andrea L. DeMaskey, and Colleen A. Smith. 2001. Selectivity
and Market Timing Performance of Fidelity Sector Mutual Funds. Financial
Review 36(1), 39–54.
Grundy, Bruce D., and J. Spencer Martin. 2001. Understanding the Nature of the
Risks and the Source of the Rewards to Momentum Investing. Review of Finan-
cial Studies 14(1): 29–78.
Jegadeesh, Narasimhan, and Sheridan Titman. 1993. Returns to Buying Winners
and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance
Moskowitz, Tobias, and Mark Grinblatt. 1999. Do Industries Explain Momentum?
Journal of Finance 54(4), 1249–90.
O’Neal, Edward S. 2000. Industry Momentum and Sector Mutual Funds. Finan-
cial Analyst Journal 56(4), 37–49.
1. Besides the author’s own analysis, this chapter is based on O’Neal (2000),
Dellva, DeMaskey, and Smith (2001), Moskowitz and Grinblatt (1999), Grundy
and Martin (2001), and Jegadeesh and Titman (1993).
Momentum in Industry Portfolios 103
2. The Sharpe ratio is based on the assumption that the portfolio under consid-
eration is held alone; hence the total risk of the portfolio, as measured by the
standard deviation, becomes relevant. The Treynor ratio, not discussed here,
relaxes that assumption. However, the Treynor ratio is more complicated to
use, as it needs estimates of systematic risk (beta) and is not commonly used
in the industry.
3. See the sub-section “Fidelity Sector Mutual Funds” under “Evidence” in this
chapter for a definition of the Sharpe ratio.
4. In addition to Fidelity and Rydex, ProFunds also offers sector funds. How-
ever, ProFunds funds are not considered, as they are relatively new.
Beyond the Random Walk104
The net asset values (NAVs) of mutual funds may be based on prices
that are several hours old. That means the NAV may not reflect the most
recent market movements. For small-cap funds with many illiquid stocks
and international funds where markets close several hours before 4 P.M.,
the NAVs may be severely mispriced, especially on volatile days when
large price movements occur.
Investors can use this information in at least one of two ways. They
can construct a trading strategy to earn abnormal returns by buying
funds when NAVs undervalue the stocks they hold and selling those
funds a few days later. Second, they can protect themselves against
other short-term traders by not investing in funds that use stale prices
while not taking steps to restrict opportunistic trading.
The net asset value (NAV) of a mutual fund is the 4 P.M. price at
which investors can purchase or redeem shares of the fund, usually
at no additional cost.1
The NAV is calculated based on the last traded
price of stocks that the fund holds. If the last trade does not take
place close to 4 P.M., the NAV may be based on stale prices and could
be incorrect. Consider a mutual fund that holds stocks of compa-
nies with small market capitalization. Since small stocks do not trade
very frequently, assume that the last trade for an average stock in
the fund takes place at 2 P.M. Now the mutual fund’s NAV calcu-
lated for 4 P.M. actually represents 2 P.M. prices. Add to that high
volatility and you have a recipe for disaster—or a market timing
opportunity. For example, on July 15, 2002, the Dow jumped more
Mispricing of Mutual Funds
Mispricing of Mutual Funds 105
than 5 percent and the Russell 2000 more than 3 percent in the last
hour of trading, between 3 P.M. and 4 P.M. A small-cap fund’s NAV
based on stale 2 P.M. prices would undervalue the fund by as much
as 3 percent. All that a smart investor had to do was to buy the fund
at the 4 P.M. closing price on July 15 and sell it the next day, pocket-
ing an abnormal return of 3 percent.
This example is an extreme one. Most NAVs do not reflect such
mispricing. Large-cap domestic funds are rarely mispriced because
large-cap stocks trade almost continuously. Even small-cap funds
are dominated by the largest of small stocks, which tend to trade
often. Moreover, there are not many days when the market jumps
3–5 percent in the last hour. And, finally, if the market is highly
volatile, then even the small stocks will trade more often, making
the last traded price more current.
On the other hand, the situation can get much worse under two
scenarios. The first is for funds that invest in foreign markets, and
the second is for funds with illiquid assets. Foreign markets close
several hours before the U.S. market closes. East Asian markets, in-
cluding Japan, close by 1 A.M. Eastern time. The European markets
close between 10 A.M. Eastern time and noon Eastern time. Thus,
the East Asian prices are about fifteen hours stale, while the Euro-
pean prices are four to six hours stale. Compounding the stale stock
prices for international funds is the staleness in exchange rates.
Funds use a variety of exchange rates: the rate at the time the for-
eign market closes, the 12 noon rate, the 4 P.M. rate, or the rate at
some other time. Thus, the mispricing of international funds can
occur more often and be of a larger magnitude.
The second condition under which the NAV can get mispriced
occurs for funds with a significant holding of illiquid assets—in
particular, private equity or restricted securities. Private equity con-
sists of shares in a non-publicly-traded firm and is usually held by
small-cap funds or venture capital funds that invest in companies
that are likely to go public. If the company does go public, the in-
vestment will generate a handsome return. However, if the brilliant
idea doesn’t materialize or the initial public offering gets delayed,
then the private equity can quickly become worthless. The problem
is that, unlike publicly traded securities, private equity is difficult
to value. Moreover, the fund manager has an incentive to delay the
write-down of private equity to avoid disclosing the magnitude of
losses. Thus, the value of private equity may be not just a few hours
stale but several months stale. If the broad market is doing well,
private equity will be undervalued, but if the market is doing poorly,
private equity will be overvalued. For example, the Van Wagoner
Table 6.1 Returns to Trading Strategy Designed to Arbitrage U.S.-Based
Mispriced Mutual Funds
Fund Type Correlation
(assets held Number Correlation with Nikkei
by fund) Observation Period of Funds with S&P (1 A.M.–4 P.M.)
1. European 06/1990 to12/1996 1 (VEURX) 0.22 —
2. European 01/1990 to 07/1998 58 0.36 —
3. European 01/1998 to 10/2001 — 0.43 —
4. European 01/1997 to 11/2000 12 0.38 —
5. European 01/1997 to 11/2000 12 0.38 —
6. Japan 01/1990 to 07/1998 17 0.25 —
7. Japan 01/2000 to 10/2001 — — 0.54
8. Japan 01/1997 to 11/2000 5 0.30 0.60
9. Japan 01/1997 to 11/2000 5 0.30 0.60
10. Pacific 06/1990 to 12/1996 1 (VPACX) 0.36 —
11. Pacific Asia 01/1990 to 07/1998 34 0.40 —
12. Pacific except 01/1998 to 10/2001 — 0.24 0.40
13. Pacific except 01/1990 to 07/1998 65 0.37 —
14. Emerging markets 05/1994 to 12/1996 1 (VEIEX) 0.11 —
15. Emerging markets 01/1990 to 07/1998 10 0.33 —
16. Foreign 02/1998 to 03/2000 139 — —
17. Domestic funds 02/1998 to 03/2000 451 — —
18. Domestic 02/1998 to 03/2000 21 — —
19. Small growth 01/1998 to 10/2001 — — —
Information in this table is based on published work listed under “References for Further Read-
Trading rule 1: Buy the international fund at the close of trading when the S&P 500’s return
exceeds its mean by more than 1.5 times the standard deviation, measured over the last forty
trading days. The fund is sold at the close on the next day, and the proceeds are kept as cash.
Trading rule 2: Buy the international fund whenever the S&P 500’s daily return is positive. Sell
the fund when the S&P 500 return is negative, and put the money in cash.
Trading rule 3: Buy the mutual fund whenever the S&P 500’s return during the last two-hour
period (1:55 P.M. to 3:55 P.M.) exceeds 0.94%. Sell the fund when the S&P 500 return is nega-
tive during the two-hour window, and put the money in cash. The number of buys is restricted
to six in this strategy, to correspond with the trading restrictions imposed. The abnormal return
is based on short-selling S&P 500 futures contracts simultaneously with mutual fund pur-
Trades Annual Annual Percent Time
Trading Per Return Return Positive Invested
Year (%) (%) (%) (%)
Mean + 1.5σ [rule 1] 18 8.9 5.3 76 7.2
S&P 500 > 0 [rule 2] 28.0 16.3 — —
Predicted return > 0 66 — 37.0 — —
Predicted return > 0.5% 18 21.7 10.8 77 13.9
Predicted return > 1.0% 3 8.8 –1.9 83 2.0
S&P 500 > 0 [rule 2] 20.5 23.8
Predicted return > 0 48.6
Predicted return > 0.5% 28 41.5 34.2 76 26.8
Predicted return > 1.0% 10 18.7 11.4 87 8.8
Mean + 1.5σ [rule 1] 18 10.1 6.5 69 7.2
S&P 500 > 0 [rule 2] 26.5 27.0
Predicted return > 0 59 50.6
S&P 500 > 0 [rule 2] 27.3 26.3
Mean + 1.5σ [rule 1] 18 12.4 9.4 88 7.2
S&P 500 > 0 [rule 2] 22.8 19.8
S&P 500 > 0.94% 6 10.4
S&P 500 > 0.94% 6 8.4 1.20
S&P 500 > 0.94% 6 21.3 5.3
Predicted return > 0 63 26.4
Trading rule 4: Buy the fund when the expected return is positive. Expected return = Corr ×
Change in the relevant market return. Sell the fund when the expected relevant market return
is negative, and put the money in cash. For European funds, the relevant market is the S&P
500 from 11:30 A.M. to 4:00 P.M.; for domestic funds, it is that day’s S&P 500 return; and for
Japanese and other Pacific Asia funds, it is the Nikkei index return from 1 A.M. to 4 P.M.
Trading rule 5: Buy the Japanese fund whenever the expected return exceeds 0.5 or 1 percent.
Expected return = Corr × [Change in Nikkei between 1 A.M. and 4 P.M]. Sell the fund when the
expected return is negative, and put the money in cash. The correlation is estimated over the
Trading rule 6: Buy the European fund whenever the expected return exceeds 0.5 or 1 percent.
Expected return = [Corr1
× Change in S&P 500 from open to noon] + [Corr2
× Change in S&P
500 from noon to close]. Sell the fund when the expected return is negative, and put the
money in cash. The correlations are estimated over the past year.
Beyond the Random Walk108
Emerging Growth Fund (VWEGX) was the target of lawsuits and
an SEC investigation for not revaluing private equity when the stock
market dropped in 2000 and 2001. While there are no reliable statis-
tics or studies that document mispricing in such funds, investors
are cautioned against holding funds that invest more than 5 percent
in private equity or other restricted securities.
Not surprisingly, past empirical evidence has uncovered numerous
instances of mispriced NAVs due to reliance on stale prices. In gen-
eral, the discovery of mispriced net asset values consists of two steps.
First, identify mutual funds whose next day’s fund return is highly
correlated with the previous day’s broad market return.Ahigh corre-
lation means that if the market return is positive today, then the fund’s
return is likely to be positive tomorrow. Second, buy the mutual fund
when the market return is large and positive, and sell the fund when
the market return becomes negative. If this trading strategy gener-
ates a significant abnormal return, then a mispricing exists.
Results of past empirical evidence are summarized in Table 6.1
for U.S.-based mutual funds. The classification of fund types is as
defined by Morningstar. The correlation of the fund return with the
market return is measured by regressing the fund return on the prior
day’s market return.2
Market return for the correlations depends on
the fund type. In the case of European funds, the S&P 500 return is
used as the market return. However, some researchers consider only
the additional U.S. return after the close of European markets. For
Japanese and Pacific funds, the Nikkei return from 1 A.M. to 4 P.M. is
most appropriate. The Nikkei return can be estimated using Nikkei
futures, traded on the Chicago Mercantile Exchange. The next col-
umn specifies the trading rule for execution of the trading strategy.
Abbreviated trading rules are given in the table.
The annual return and the abnormal return in the table are not
annualized returns; rather, these returns are earned during the time
that the mispriced fund is held. If the fund is held for less than a full
year, then the corresponding risk is also less. For example, in row 5,
a return of 8.8 percent is earned by investing for only five days in a
whole year or by investing for only 2 percent of the time. The ab-
normal return for this trading strategy is –1.9 percent because the
one-year buy-and-hold return for someone who is fully invested is
10.7 percent. Obviously, an investor invested for only 5 days has
much lower risk than one who invests for 250 days in a year. Thus,
Mispricing of Mutual Funds 109
in many cases the abnormal return is misleading because it does
not account for risk or the holding period. It is important to note
that all of these trading strategies have less risk than being fully
invested, because an investor employing these strategies will be
holding cash for a significant period of time.
Table 6.1 reveals a high level of correlation between the S&P 500
or the Nikkei index and the next day’s net asset values of funds.
Correlations of 0.3 or 0.4 between same-day returns are not consid-
ered large. But a correlation between the current return and the pre-
vious day’s return of 0.3 to 0.6 is extremely high and seemingly
profitable. The following table, based on data from January 1990 to
July 1998, illustrates the importance of the high lagged correlations:
Average daily return if Average daily return if
previous day’s S&P 500 previous day’s S&P 500
return is positive is negative
Emerging market funds 0.17 –0.17
Pacific Asia funds 0.20 –0.23
Europe funds 0.21 –0.14
Japan funds 0.15 –0.21
The table shows that positive S&P 500 days are followed by posi-
tive return days for the international funds. Isn’t it amazing that
today’s S&P 500 return can tell us so much about tomorrow’s mea-
sured return for international funds? Even Japanese funds that de-
clined during this period would have earned high positive returns
by selective investing. As you will see, this pattern is borne out by
the profitability of trading strategies.
Returning to Table 6.1, we can see that the annual return varies
from 8.4 percent to 41.5 percent, while the abnormal return ranges
from –1.9 percent to 50.6 percent.3
The reason for the negative ab-
normal return, as discussed above, is the extremely short holding
period of 5 days, or 2 percent of the entire year. In the case of the
Japanese funds in row 8, an annual return of 41.5 percent could
have been earned by holding the funds for only 67 days in a whole
year. The trading strategies are profitable between 69 percent and
88 percent of the time. This success ratio compares favorably with a
normal buy-and-hold strategy that has a maximum of 55 percent
days with positive returns. It can also be seen from the table that the
results vary considerably across fund types, observation periods,
and trading rules.
Beyond the Random Walk110
The trading rules used in Table 6.1 are summarized below:
Trading rule 1: Buy the international fund at the close of trading when the
S&P 500’s return exceeds its mean by more than 1.5 times the standard de-
viation, measured over the last forty trading days. The fund is sold at the
close on the next day and the proceeds are kept as cash.
Trading rule 2: Buy the international fund whenever the S&P 500’s daily
return is positive. Sell the fund when the S&P 500 return is negative, and
put the money in cash.
Trading rule 3: Buy the mutual fund whenever the S&P 500’s return during
the last two-hour period (1:55 P.M. to 3:55 P.M.) exceeds 0.94 percent. Sell the
fund when the S&P 500 return is negative during the two-hour window,
and put the money in cash. The number of buys is restricted to six in this
strategy, to correspond with the trading restrictions imposed. The abnor-
mal return is based on short-selling S&P 500 futures contracts simultaneously
with mutual fund purchases to reduce risk (also see Appendix C).
Trading rule 4: Buy the fund when the expected return is positive.
Expected return = Corr × Change in the relevant market return.
Sell the fund when the expected relevant market return is negative, and
put the money in cash. For European funds, the relevant market is the S&P
500 from 11:30 A.M. to 4:00 P.M.; for domestic funds, it is that day’s S&P 500
return; and for Japanese and other Pacific funds, it is the Nikkei index return
from 1 A.M. to 4 P.M. Corr is the correlation between the fund return and the
relevant market return. The correlations are estimated over the past one year.
Trading rule 5: Buy the Japanese fund whenever the expected return ex-
ceeds 0.5 percent or 1 percent.
Expected return = Corr × Change in Nikkei between 1 A.M. and 4 P.M.
Sell the fund when the expected return is negative, and put the money in
cash. The correlation is estimated over the past one year.
Trading rule 6: Buy the European fund whenever the expected return ex-
ceeds 0.5 percent or 1 percent.
Expected return = [Corr1
× Change in S&P 500 from open to noon] +
× Change in S&P 500 from noon to close]
Sell the fund when the expected return is negative, and put the money in
is the correlation between the fund return and the S&P 500 re-
turn from open to noon, while Corr2
is the correlation between the fund
return and the S&P 500 return from noon to close. The correlations are esti-
mated over the past one year.
Mispricing of Mutual Funds 111
Trading rules that trigger execution of a strategy come in various
styles. The simplest trading rule—to buy the fund if the S&P 500
return is positive and sell the fund if the sign is negative (rule 2)—
applies to rows 2, 6, 11, 13, and 15. For this trading rule, only the
sign of the raw S&P 500 return is considered. This strategy has the
highest or second highest return within each fund type. This strat-
egy will also have the highest number of trades and be invested for
the longest period of time, which is not desirable. A related trading
rule is rule 3, where the threshold return is not zero but 0.94 per-
cent, as for rows 16–18.4
Besides static trading rules, a dynamic trad-
ing rule, in which the mean and standard deviation are calculated
every day based on the previous forty trading days (rule 1), applies
to rows 1, 10, and 14. A trade is signaled when the S&P 500 return
exceeds the mean by 1.5 standard deviations.
Rules 1, 2, and 3 discussed above do not consider the actual cor-
relation between the fund return and the prior period’s market re-
turn. Instead, they are based on the absolute value of the market
return. Since the correlation between the fund and the market con-
tains information regarding the expected movement in the NAV,
rules 4, 5, and 6 use the information contained in the correlation by
computing a predicted return. For example, the predicted return
for the next day used in rule 6 for rows 4 and 5 is calculated as the
correlation between the S&P 500 return and the fund return multi-
plied by the S&P 500 return for day t.
If the predicted return is positive, as for rule 4, or greater than 0.5
percent or 1.0 percent, as for rules 5 and 6, the buy signal is triggered.
The period over which the correlation between the market return and
the fund return is estimated should ideally be about a year.
Trading rules 5 and 6 allow a comparison of how the threshold
return affects the results. Compared to a lower threshold of 0.5 per-
cent, a higher threshold of 1 percent generates fewer trades, a smaller
annual return, a higher success ratio, and fewer days for which the
fund is held. For example, row 9, with a 1 percent threshold return,
generates only ten trades, a return of 18.7 percent, and a success
ratio of 87 percent by investing for only 8.8 percent of the time. On
the other hand, row 8, with a 0.5 percent threshold, generates twenty-
eight trades, a return of 41.5 percent, and a success ratio of 76 per-
cent for a 26.8 percent investment period. Thus, depending on the
restrictions placed by the fund, the threshold can be altered to ob-
tain an optimal number of trades that maximizes the return earned
without alerting the mutual fund management.
The profitability of trading strategies varies considerably by fund
type and depends on the market chosen as relevant. When the S&P
Beyond the Random Walk112
500 return is used to signal buys and sells, Japanese funds outper-
form European funds in the case of rule 1, but European funds out-
perform Japanese funds with rule 2. However, if the Nikkei index is
relied upon for signaling trades, Japanese and other Pacific Asia
funds outperform European funds.
Domestic funds can also be profitable, but the profitability is much
less than for foreign funds. Among domestic funds, small-cap and
high-risk (beta) funds are the most attractive.
Generally, arbitrageurs can earn an annual return of 10–50 per-
cent by arbitraging mispriced mutual funds. This return comes at
significantly lower risk than for a fully invested portfolio, but the
return estimates assume negligible trading costs and no restrictions
on trading. In particular, the following fund types are likely to be
mispriced and are ordered from high to low level of mispricing.
1. Funds heavily invested in Japanese and Pacific markets
2. Funds heavily invested in European markets
3. Funds invested in other foreign markets
4. Funds with a high fraction of private equity
5. Funds with a small median market capitalization
6. Funds that hold high-risk stocks (that is, stocks that move more
than the market)
7. Funds with high market-to-book ratio
There are two limitations of this evidence. First, most of the work is
based on the data from the 1990s. The last decade was unique be-
cause the correlations among different markets were higher than
usual. Since the profitability of trading strategies depends on the
level of correlation, the returns earned would fall if the actual corre-
lations during the current period are lower.
The second and possibly more important limitation relates to trad-
ing costs and restrictions. A few years ago it was possible to execute
numerous trades without any restrictions. However, an increasing
number of funds are imposing short-term redemption fees and lim-
iting the number of round-trip trades that an investor can make in a
year. Nonetheless, hundreds of funds still exist where no redemp-
tion fees are charged. Other kinds of trading restrictions, such as
monitoring an individual account for the number of trades, are easy
Mispricing of Mutual Funds 113
to overcome by routing trades through a supermarket, such as
Charles Schwab or TD Waterhouse. Loads and redemption fees
imposed by funds are more difficult to avoid. However, it is profit-
able to time the mutual funds even after payment of short-term trad-
ing fees, as shown in the section on “Strategy Implementation” later
in this chapter.
The main reason for mispricing of mutual fund NAVs is that the
fund managers do not care or do not have acceptable solutions to
eliminate mispriced NAVs. The background and the current solu-
tions are discussed to highlight the reasons for persistence.
The mispricing of mutual funds took center stage during the East
Asian currency crisis, when stock prices were flip-flopping. On Oc-
tober 27, 1997, the S&P 500 fell nearly 7 percent. The next morning,
due to worsening conditions in East Asia and the drop in the S&P
500, the Hong Kong stock market fell 14 percent. However, the U.S.
market, instead of falling further, rallied 5 percent on October 28,
1997. Since the U.S. market leads foreign markets, the Hong Kong
market was expected to rally, and the futures prices for the Hong
Kong stock market showed that the market would indeed rally.
Many investors, believing that the Hong Kong market was under-
valued or because they wanted to time the mutual funds, bought
mutual funds exposed to Hong Kong on October 28, 1997, at their
NAVs. The funds included Fidelity China Region Fund (FHKCX,
with Hong Kong as the primary investment area), Investec China
and Hong Kong Fund (ICHKX), U.S. Global China Region Oppor-
tunity (USCOX), and T. Rowe Price New Asia Fund (PRASX). Many
investors who bought mutual funds exposed to Hong Kong on that
day profited from their positions. ICHKX fell 11 percent on October
28, 1997, and rose 15 percent the next day; USCOX fell 10 percent on
October 28, 1997, and rose 9 percent the next day; and PRASX fell 9
percent on October 28, 1997, and rose 9 percent the following day.
Since these investors captured the return on October 29, 1997, they
earned 9 percent to 15 percent in one day.
However, changes in Fidelity’s Hong Kong fund were much
smaller, with a fall of 5 percent on October 28, 1997, and a rise of
only 2 percent the following day. Why did Fidelity’s Hong Kong
fund show much lower volatility? Because Fidelity relied on fair
value pricing, whereas the other fund families did not. With fair
value pricing, Fidelity used stock futures prices to value the Hong
Beyond the Random Walk114
Kong fund, reducing the staleness in its NAV. On the negative side,
Fidelity could not report the NAV to Nasdaq until two days later
because of intricate calculations required in the computation of fairly
valued NAV. Moreover, and for all practical purposes, Fidelity did
not allow trades on either October 28 or October 29, 1997.
The above incident illustrates that fund companies have been
aware of mispriced net asset values for a long time. At the same
time, it highlights the pros and cons of fair value pricing. There are
many solutions to mispricing, as described below, in addition to
fair value pricing. Though these solutions reduce the benefits from
arbitraging any mispricing, they are either difficult to implement or
do not completely eliminate opportunities for arbitrage.
POSSIBLE SOLUTIONS TO MISPRICING
Short-Term Redemption Fees
About 60 percent of international funds have adopted short-term
redemption fees. With redemption fees, an investor is required to
pay a fee ranging from 0.50 percent to 2.0 percent to the fund if the
investment is liquidated in less than thirty or ninety days. While
redemption fees can reduce the profitability and frequency of arbi-
trage trades, they have other shortcomings. First, investors don’t
like them because it takes away their ability to use mutual funds for
parking money. Instead of bank accounts, many customers use bro-
kerage accounts and write checks against the funds they hold. If
investors are unable to redeem funds at will, it reduces the attrac-
tiveness of mutual funds as an investment vehicle. Second, many
arbitrage trades are profitable even after allowing for redemption
fees.Alternatively, arbitrageurs can wait out the redemption fee and
still earn the abnormal returns, albeit at a higher risk. For example,
the arbitrageur can hold the fund for thirty days if the short-term
fee applies for holding periods less than thirty days. As Table 6.1
shows, many strategies require as few as six trades per year to earn
an abnormal return of more than 10 percent per year.
Restrictions on Trading Frequency
A majority of funds either explicitly limit the number of trades per
year or warn investors against frequent trading. As in the case of
redemption fees, such restrictions reduce the attractiveness of funds
to ordinary investors. However, it is easy to hide behind mutual
fund supermarkets, such as Charles Schwab, TD Waterhouse,
Mispricing of Mutual Funds 115
Scottrade, and Brown and Co. Mutual fund supermarkets are usu-
ally permitted to indicate to the fund family a single consolidated
trade for all of their accounts at the end of each trading day. As a
result, the responsibility for monitoring the frequency of trades is
delegated to the fund supermarket. However, supermarkets fail to
perform this function effectively as long as the net trade amounts
are not unusually large. In addition, it is very easy to shift money
from one fund family to another without running afoul of trading
restrictions imposed by the fund families.
Front-End Loads and Back-End Loads
Some people believe that load funds do not allow timing of mutual
funds. This is true for arbitrageurs trying to time funds of different
fund families. However, it is easy to time funds within a fund fam-
ily because many of them allow unrestricted trading among their
own family’s funds once the investor puts his or her money in the
fund family. Since almost all mutual fund families have an S&P 500
index fund as well as several foreign funds, it is easy for an investor
to use the trading strategies outlined earlier. In addition, fund fami-
lies do not usually impose loads on monies held in retirement ac-
counts. Individual investors can use retirement accounts to time
funds with stale NAVs.
Besides the inability to discourage timing, imposition of loads
discourages investors from investing in the fund family because
load funds do not generate superior performance when compared
with no-load funds. Although opportunities for timing are reduced,
loads are not normally favored by fund families as a way of limit-
ing trading frequency.
Restricting the Trading Time
Another solution is not to allow trading in foreign funds while the
U.S. market is open. For example, the last order for a foreign fund
can be restricted to 9:30 A.M. Such time restrictions can reduce the
opportunity for arbitrage, but they suffer from at least three limita-
tions. Investors may not want to be constrained by the trading time.
Second, the futures prices provide a reasonable approximation of
the likely movement in stock prices. For example, the Nikkei fu-
tures contract before 9:30 A.M. can still capture anticipated move-
ments in Japanese and other Pacific funds. Finally, stale prices also
occur within a market, as shown in the last three rows of Table 6.1.
Therefore, time restrictions may not be very effective in preventing
arbitrage of mispriced mutual funds.
Beyond the Random Walk116
Fair Value Pricing
All of the solutions listed above try to prevent arbitrageurs from
timing purchases and sales but do not really tackle the underlying
problem of mispricing. Fair value pricing attempts to fairly value
mutual funds. Instead of using stale prices, fund companies would
update the stale prices with market movements to obtain a fair net
asset value. The fair value pricing could be done for each individual
security or for the fund as a whole. The idea is to make the correla-
tion between the fund’s return and the previous day’s market re-
turn as close to zero as possible. If the correlation is zero, arbitrageurs
cannot predict movements in fund net asset values, thereby elimi-
nating any profit opportunities.
While the intuition behind fair value pricing is simple, implemen-
tation is another matter. The relevant market for a stock or a fund is
not obvious. Some stock prices or fund NAVs may depend on mul-
tiple markets rather than just the S&P 500. And the correlation be-
tween a fund and a particular market may not be constant but may
change continuously. Even when the relevant market is known and
stable, there may be no way of accurately measuring the market’s
return. For example, small-cap stocks are correlated more closely with
the Russell 2000 than with the S&P 500. But Russell 2000 exchange-
traded funds and futures contracts themselves have stale prices be-
cause of low trading volume. In addition, imagine the computational
complexity required at the end of each day. A delay of two days for
pricing, as in the case of Fidelity in 1997, is generally unacceptable.
If fair value pricing is so complex, perhaps funds could use it only
on days when there is extreme market movement. Some fund com-
panies do selectively apply fair value pricing; selective application is
good for publicity but does little else. Big price moves that warrant
fair value pricing occur once or twice a year at best and account for
less than 10 percent of the total arbitrage profit that can be earned.
The remaining 90 percent can still be captured by the arbitrageurs by
making numerous though relatively low-profit trades.
The Trading Process
How do you profitably trade mispriced mutual funds? The first step
consists of identifying mispriced funds. This is followed by execu-
tion of an appropriate trading strategy. The process of discovering
and trading mispriced funds described here is based only on a single
index, the S&P 500. To extend the process to use other indexes or
even multiple indexes, change the regressions in steps 5 and 7.
Mispricing of Mutual Funds 117
Step 1: Pick mutual funds that you are interested in. The size of
the initial set of mutual funds will depend on computational and
data resources. If resources permit, start with as large a data set as
possible. The largest data set consists of more than fifteen thousand
Step 2: Exclude funds with less than $10 million in assets because
their returns are likely to be very volatile. Also, exclude funds that
are less than two years old because you will need at least two years
of data to estimate the regressions. Keep only equity funds as the
results documented above relate to equity funds alone. If it is not
possible to screen out funds based on these criteria, keep the entire
initial set and eliminate them from the short list that you would
create in step 8.
Step 3: Obtain daily historical S&P 500 returns, including distri-
butions such as cash and stock dividends. The S&P 500 index levels
only give the returns excluding distributions. The daily returns in-
cluding distributions can be obtained from Standard and Poor’s.
Unfortunately, the data are not available on their website, and they
charge exorbitant fees for even small bits of data. A close approxi-
mation to the total S&P 500 return can be obtained by using the
prices of the Vanguard 500 Index Fund (VFINX), adjusted for distri-
butions that are available on Vanguard’s website.
Step 4: Obtain historical daily fund prices adjusted for distribu-
tions for the funds you keep after step 2. It is especially important
here to make sure that adjustments for distributions have been made.
Most websites, including Yahoo!, do not accurately account for dis-
tributions such as cash dividends and capital gains distributions
(see “Internet Resources” for data sources). Compute returns from
daily fund prices.
Step 5: Run a regression of each fund’s daily return on the previ-
ous day’s S&P 500 return using the previous year’s data. The previ-
ous year need not be a calendar year—only twelve consecutive
months are needed. If you have only a few funds (ten to fifteen), the
regression can be run in Microsoft Excel under Data Analysis.5
you have hundreds of funds that you are researching, a more pow-
erful software package is required.6
In the regression, only the pre-
vious day’s S&P 500 return has been specified. However, that is not
ideal. International funds are likely to be influenced by other in-
dexes such as the Nikkei and will be more affected by the afternoon
S&P returns than the whole day return. Small-cap domestic funds
are affected by movements in the Russell 2000. These refinements
are desirable but have not been included here in order to keep the
implementation relatively simple and more accessible.
Beyond the Random Walk118
Step 6: Select funds with a coefficient (also called correlation in
earlier sections of this chapter) of at least 0.30 on the previous day’s
S&P 500 return. Coefficients with higher values are preferred. In
addition, make sure that the explained sum of squares (R-squared)
is at least 10 percent.
Step 7: For the selected funds, redo the analysis in step 5 based on
data for the year two years prior to the current year. This allows
you to verify that the high correlation is persistent and not for just
one year. Drop the funds that do not exhibit a coefficient of at least
0.30 and an R-squared of at least 10 percent.
Step 8: Take the short list of funds from the previous step and
research their loads, redemption fees, and trading restrictions, if any.
Keep only those funds that can be traded easily, preferably without
any fees. If you end up with many funds, choose the ones with more
assets (at least $10 million) and with higher coefficients. The num-
ber of funds will depend on trading fees, your investment amount,
and the amount of risk you are willing to accept. If you choose only
one fund, the strategy will be riskier than for a portfolio of five to
Step 9: Set up a trading strategy that uses each fund’s parameter
estimate or coefficient. Say that the coefficient is 0.40. Then the pre-
dicted return for the next day for that fund = 0.40 × current S&P 500
Step 10: Initially, begin with a trading strategy that buys if the
predicted return is at least 1 percent. Sell when the predicted return
is less than –0.10 percent. Based on the past year, calculate the num-
ber of trades that would be triggered by the strategy. If the fund will
allow more trades, then lower the minimum predicted return from
1 percent to 0.75 percent. If there are too many trades, increase the
minimum predicted return. Don’t become very exact in choosing
the threshold because return characteristics for the holding period
are bound to be different.
Step 11: Do a dry run for about a month with the selected funds to
become comfortable with the fund and to gain confidence in your
strategy. If you like the results, go live!
The above investment strategy is implemented in this section. The
initial sample consists of 14,445 mutual funds, including equity,
bond, and hybrid funds. Any nonequity funds will be automati-
cally eliminated because their correlation with the S&P 500 is likely
Mispricing of Mutual Funds 119
to be less than 0.30. If they still remain, they will be removed when
the characteristics of each short listed fund are verified.
DISCOVERY OF MISPRICED FUNDS
Each fund’s return for 2001 is regressed on the previous day’s S&P
500 return. Funds that have a parameter estimate or coefficient on
the lagged S&P 500 return of greater than 0.30 are selected. Out of
an initial set of 14,445 funds, 607 have a parameter estimate greater
than 0.30. The regressions and the screening are repeated with data
from 2000. In this way, it can be ensured that the relationship that is
observed in 2001 also existed in 2000. Again, the parameter esti-
mate must be greater than 0.30. The number of funds that survive
falls to 379. Besides elimination due to an unstable coefficient, some
funds are lost because they did not exist in 2000.
Data relating to fund characteristics such as assets under man-
agement, category, and so on for the 379 funds is obtained from
Morningstar’s Principia Pro for December 2001 or from Standard
and Poor’s. Once these data are collected, two other conditions are
imposed. First, the assets under management must exceed $10 mil-
lion. With this screen, the number of funds falls to 245. Second, at
least 10 percent of the return must be explained by the previous
day’s S&P 500 return. In other words, the R-squared from a regres-
sion must be at least 10 percent for both 2000 and 2001. A total of
214 funds satisfy this condition.
The top ten funds in each category, ranked by the average corre-
lation for 2000 and 2001, are tabulated in Table 6.2, without regard
to trading restrictions. Table 6.1 shows that trading restrictions re-
duce but do not eliminate the profitability. The restrictions are explic-
itly considered later in Tables 6.4 and 6.5. Some fund families have
multiple classes for the same fund. Since fund classes vary only in
loads and expenses, but really pertain to the same underlying portfo-
lio, only the fund that is least restrictive in terms of trading is se-
lected. Three categories are considered based on Morningstar’s
definitions: foreign, Europe, and Pacific Asia. The foreign category
includes funds that are international in nature and not confined to a
The thirty funds listed in Table 6.2 show significant mispricing.
The regression coefficient varies from 0.34 to 0.69 for European
stocks, from 0.32 to 0.57 for foreign stocks, and from 0.37 to 0.57 for
Pacific Asia stocks. These coefficients are based on using the lagged
S&P 500 return, though it may not necessarily be the relevant mar-
ket for international funds. As mentioned earlier, using other mar-
ket indexes or futures such as the Nikkei or Eurotop in the regression
might improve the predictability.
Table 6.2 List of Top Ten Short-listed Funds by Category
These funds are ones whose prices are most mispriced. The estimate of mispricing is based on a regression of fund return on the lagged S&P
500 return for the years 2000 and 2001. Ten funds in each category with the largest coefficients and an R-squared of greater than 10% are
Ticker Fund Name Fund Size Coeff. 2001 R2
2001 Coeff. 2000 R2
PEAGX Payden European Aggressive Growth 13.6 0.69 0.18 0.62 0.13
FEURX INVESCO European Investor Class 352.9 0.41 0.12 0.55 0.15
AEDCX AIM European Development C 32.9 0.34 0.15 0.59 0.18
GTGEX AIM Euroland Growth A 212.4 0.40 0.11 0.52 0.13
PRBEX Prudential Europe Growth B 57.0 0.42 0.13 0.43 0.15
UMPNX Excelsior Pan European 63.4 0.36 0.13 0.46 0.20
LMEUX Legg Mason Europe C 24.0 0.38 0.11 0.43 0.12
FNORX Fidelity Nordic 103.8 0.38 0.13 0.43 0.11
LMEFX Legg Mason Europe A 32.7 0.38 0.11 0.42 0.12
ANECX Alliance New Europe C 35.0 0.34 0.10 0.42 0.15
HAIGX Harbor International Growth 405.9 0.57 0.18 0.51 0.14
PJRCX Prudential Jenn International Growth C 24.1 0.54 0.17 0.53 0.13
CSQBX Smith Barney International 65.0 0.39 0.13 0.62 0.20
Aggressive Growth B
STISX Strong International Stock 77.5 0.30 0.15 0.65 0.23
FPSSX Dreyfus Founders Passport F 79.0 0.32 0.15 0.61 0.22
LINCX Lord Abbett International C 11.4 0.43 0.20 0.50 0.22
SBIEX Smith Barney International All Cap 199.1 0.40 0.14 0.52 0.14
UISLX UM International Small Cap Equity 10.5 0.37 0.16 0.54 0.25
PRITX T. Rowe Price International Stock 6,370.5 0.32 0.12 0.37 0.21
TWEGX American Century International 1,016.0 0.36 0.22 0.56 0.20
WPJGX Credit Suisse Japan Growth Fund 52.5 0.57 0.11 0.81 0.15
ICHKX Investec China and Hong Kong 77.1 0.51 0.15 0.80 0.30
PCASX Pacific Cap New Asia Growth Y 19.6 0.51 0.16 0.68 0.29
EMCGX Eaton Vance Greater China Growth B 42.3 0.45 0.15 0.67 0.27
MSCAX Van Kampen Asian Equity C 15.5 0.47 0.16 0.64 0.26
MSAEX Morgan Stanley Asian Equity A 49.0 0.45 0.15 0.63 0.25
SCOPX Scudder Pacific Opportunity S 76.9 0.40 0.13 0.66 0.26
MDDRX Merrill Lynch Dragon D 48.0 0.39 0.13 0.59 0.22
PRASX T. Rowe Price New Asia 527.2 0.38 0.10 0.60 0.26
ASIBX AIM Asian Growth B 28.1 0.37 0.16 0.60 0.23
Table 6.3 Returns from Trading Mispriced Mutual Funds
During January–June 2002
Predicted Return >0.5% Predicted Return >0.5%
and 1-Day Holding Period and 2-Day Holding Period
6-Month Number Success 6-Month Number Success
Return of Ratio Return of Ratio
Ticker (%) Trades (%) (%) Trades (%)
Vanguard Fund 1.2 9 33.3 0.1 7 42.9
Panel A: European Funds
PEAGX 22.7 27 81.5 6.7 21 66.7
PRBEX 12.7 15 73.3 8.2 11 72.7
FEURX 11.8 14 64.3 7.1 11 54.5
GTGEX 14.2 14 92.9 9.8 11 63.6
LMEFX 11.0 14 78.6 7.3 11 54.5
LMEUX 10.8 14 78.6 7.4 11 54.5
FNORX 11.7 14 92.9 8.4 11 63.6
UMPNX 12.8 14 85.7 9.2 11 63.6
AEDCX 9.0 11 90.9 7.1 9 88.9
ANECX 10.0 12 75.0 5.7 10 60.0
Total Europe 12.7 15 81.3 7.7 12 64.3
Panel B: Foreign Funds
HAIGX 9.1 24 66.7 2.2 19 63.2
PJRCX 13.3 23 69.6 7.4 19 57.9
LINCX 10.0 15 86.7 8.0 11 81.8
SBIEX 11.9 14 85.7 8.7 11 45.5
CSQBX 12.4 14 92.9 7.1 11 54.5
UISLX 10.2 14 78.6 9.7 11 81.8
FPSSX 6.8 9 88.9 7.3 7 71.4
PRITX 8.5 9 66.7 6.1 7 57.1
PINMX 7.8 9 66.7 6.2 7 57.1
STISX 7.4 9 55.6 5.1 7 57.1
TWEGX 11.2 13 84.6 8.5 10 60.0
Total Foreign 10.1 14 77.6 7.1 12 63.0
Panel C: Pacific Asia
WPJGX 26.3 24 66.7 17.3 19 57.9
ICHKX 14.2 21 52.4 14.0 17 58.8
PCASX 18.2 21 71.4 18.5 17 64.7
MSCAX 12.7 18 72.2 11.0 14 57.1
EMCGX 11.1 17 58.8 8.9 13 46.2
MSAEX 13.2 17 70.6 9.8 13 53.8
MDDRX 12.6 14 71.4 7.8 11 45.5
SCOPX 13.6 14 71.4 10.0 11 45.5
PRASX 5.7 14 50.0 3.0 11 45.5
ASIBX 11.5 13 84.6 7.8 10 60.0
Total Pacific Asia 13.9 17 67.0 10.8 14 53.5
Total All 30 Funds 12.2 15 75.3 8.5 13 60.3
The first row reports the return for the S&P 500 as provided by the Vanguard fund. The remain-
ing information is from trading funds identified in Table 6.2.
Beyond the Random Walk124
RETURNS FROM TRADING MISPRICED FUNDS
Once the grossly mispriced funds are identified using data from
2000 and 2001, actual returns from trading these funds during the
subsequent six months are estimated and reported in Table 6.3. The
following four strategies are employed. In all cases, the predicted
return for the next day is calculated as the coefficient for 2001 times
the current S&P 500 return. Since orders for mutual funds must be
placed by 4 P.M., in reality, the S&P 500 return until 3:55 P.M. only
will be considered. It is highly unlikely that the signal will change
based on the S&P 500’s movement during the last five minutes.
The four strategies are:
• Buy the fund when the predicted return for the next day is at
least 0.5 percent, with a holding period of one day—that is, the
fund will be sold the next day.
• Buy the fund when the predicted return for the next day is at
least 0.5 percent with a holding period of two days. Some fund
supermarkets do not allow investors to sell the fund until the
day after it is settled. Settlement takes one business day for
most mutual funds.
• Buy the fund when the predicted return for the next day is at
least 1 percent, with a one-day holding period.
• Buy the fund when the predicted return for the next day is at
least 1 percent, with a two-day holding period.
The first trading strategy (0.5 percent and one day) is the most
profitable, as it imposes the fewest constraints on trading. The top
ten European funds yield a return of 12.7 percent in 6 months com-
pared with a buy-and-hold return of –7.7 percent. This is equiva-
lent to an abnormal return of 20.4 percent for 6 months, or more
than 40 percent per year. The success ratio is 81.3 percent. By com-
parison, a similar strategy employed for the Vanguard 500 Index
Fund, as a proxy for the S&P 500, would have generated a return of
1.2 percent. Foreign funds and Pacific Asia funds are similar, with
abnormal returns of 15.2 percent and 11.7 percent over six-month
The returns are smaller for the other three strategies, although
the success ratio improves for funds with more than three or four
trades when the threshold is 1 percent. The two-day holding period
returns for the selected categories are 7.7 percent for European funds,
7.1 percent for foreign funds, and 10.8 percent for Pacific Asia funds.
In most cases the returns for 2002 correspond closely with the co-
Mispricing of Mutual Funds 125
efficients reported in the last column. The close association between
the January-June 2002 returns and the 2001 coefficients suggests that
the pattern of returns is quite stable between 2001 and 2002 and is
indicative of the future profitability of similar trading strategies.
The results in Table 6.3, shown in Figure 6.1, strongly suggest
that mispricing of mutual funds can be exploited in real time.
RETURNS FROM MISPRICED FUNDS WITH NO TRADING RESTRICTIONS
Until now, trading restrictions have not been explicitly considered.
They can reduce the profitability of strategies that require frequent
trading. To account for any trading restrictions, all funds that have
any kind of restriction on trading are excluded. Among the remain-
ing funds, five funds are selected that have the highest estimated
regression coefficients. The selected funds are in the first row of
With the least restrictive trading strategy, these funds would have
earned an average return of 6.9 percent over the January–June 2002
six-month period with a success ratio of 67.8 percent, compared to
an average return of –0.6 percent for a buy-and-hold investor. The
two-day return is 4.5 percent with a 0.5 percent threshold and –0.1
percent with a 1.0 percent threshold. The 1.0 percent threshold is
probably too high, as it results in an average of only two trades over
Figure 6.1 The returns from trading mispriced funds are compared with the fund’s
buy-and-hold return over the January-June 2002 period.
European funds Pacific Asia funds
Returns from Trading Mispriced Funds
Buy and hold
Table 6.4 Returns from Trading the Top Five Mutual Funds by Mispricing*
Ticker HAIGX PRASX STISX FPSSX NAGUX Total
Loads 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Redemption fees 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Fund return –7.6% 6.1% –5.1% 4.1% 0.3% –0.6%
S&P 500 return –13.2% –13.2% –13.2% –13.2% –13.2% –13.2%
1-Day Holding with Predicted Return > 0.5%
Return 9.1% 5.7% 7.4% 6.8% 5.5% 6.9%
No. of trades 24 14 9 9 9 13
Success ratio 66.7% 50.0% 55.5% 88.9% 77.8% 67.8%
2-Day Holding with Predicted Return > 0.5%
Return 2.2% 3.0% 5.1% 7.3% 4.8% 4.5%
No. of trades 19 11 7 7 7 10
Success ratio 63.2% 45.5% 57.1% 71.4% 71.4% 61.7%
2-Day Holding with Predicted Return > 0.5%—Hedged
Return 6.5% 3.3% 3.8% 6.0% 3.7% 4.7%
No. of trades 19 11 7 7 7 10
Success ratio 52.6% 45.5% 57.1% 57.1% 42.9% 51.0%
2-Day Holding with Predicted Return > 1.0%
Return 4.7% –5.5% –0.7% 0.4% 0.4% –0.1%
No. of trades 7 2 1 1 1 2
Success ratio 71.4% 0.0% 0.0% 100.0% 100.0% 54.2%
2-Day Holding with Predicted Return > 1.0%—Hedged
Return 3.3% –4.2% 0.8% 1.8% 2.1% 0.8%
No. of trades 7 2 1 1 1 2
Success ratio 42.9% 0.0% 0.0% 100.0% 100.0% 68.6%
*All numbers are reported for the six-month period, January to June 2002.
Mispricing of Mutual Funds 127
a six-month period. However, the results for 0.5 percent and 1.0 per-
cent thresholds are reported throughout this chapter.
The trading strategy is designed to predict the next day’s return.
However, sometimes investors are forced to hold the fund for two
days and thus are exposed to unnecessary market movements on
the second day. This risk can be reduced if the investor short-sells
S&P 500 futures (or SPDRs) when he buys the fund at 4 P.M. on day
0. He would close the short position in S&P 500 at the close of day 1
and sell the fund at the close on day 2. In this way, any movement in
the mispriced fund on day 2 due to S&P 500’s return on day 1 is
partially neutralized by the short position. The result is a hedged
The hedged two-day return with 0.5 percent and 1.0 percent
thresholds are in Table 6.4 and show that the success ratio of a hedged
strategy is not necessarily better. The return to a hedged strategy
improves slightly primarily because the S&P 500 was falling during
this period. In any case, and despite the mixed results, the hedged
return has much less exposure to the market and therefore less risk
than the unhedged return. More details about hedging market risk
are in Appendix C.
RETURNS FROM A FUND WITH A REDEMPTION FEE
It is possible to gain from mispricing even if you are not allowed to
trade the fund for a prespecified period without paying a redemp-
tion fee. There are two approaches.
Wait Out the Redemption Fee
The basic idea behind the first approach is to wait out the minimum
holding period. You would earn an abnormal return with each trade
that you use to enter the fund, and then earn a normal return for the
remaining holding period. With a thirty-day holding period, you
may be able to execute between eight and eleven trades in a year.
With an abnormal return of about 1.5 percent per trade, the annual
abnormal return is likely to be approximately 12 to 15 percent.
As an illustration, consider the Payden European Aggressive
Growth Fund (PEAGX), which has a coefficient of 0.69. The trading
strategy is as follows:
• If the predicted return is greater than 1 percent, buy PEAGX.
• Sell the fund at the end of the holding period if the predicted
return for that day is less than –0.1 percent.
• Repeat this process.
Beyond the Random Walk128
The results are reported in Table 6.5 for a thirty-day holding pe-
riod. There are four signals during January–June 2002 with a 1.0
percent threshold. The total return is –5.8 percent. Compared with a
buy-and-hold return of –17.1 percent, an investor would have earned
an abnormal return of 11.3 percent over the six-month period,
equivalent to an annual abnormal return of 22.6 percent even for a
fund that has a thirty-day redemption fee. It is clear that a timing
strategy is superior to a buy-and-hold strategy.
Pay the Redemption Fee
The second approach is to actually sell the fund even if you have to
pay the redemption fee. However, the redemption fee is paid only
when the predicted return is more negative than the redemption
fee. Assuming a 1 percent redemption fee, there are eight buy sig-
nals for PEAGX over the January–June 2002 period. Seven of the
Table 6.5 Returns for a Mispriced Fund with Redemption Fee
Fund Name and Details
Payden European Aggressive Growth (PEAGX)
Period: January to June 2002.
Buy-and-hold return = –17.1% for 6 months
Correlation based on 2001 = 0.69
S&P 500 return = –13.2% for 6 months
A redemption fee of 1% applies if the fund is held for less than 30 days
Buy signal when the predicted return > 1.0% for both strategies below.
Wait out the redemption fee. That is, once the fund is bought, it is not sold
for 30 days.
Number of trades = 4
Return based on signals and holding for at least 30 days = –5.8%
Abnormal return = 11.3% for 6 months
Pay the redemption fee if the predicted return is less than the redemption fee,
that is, < –1.0%
Number of trades = 8
Gross return based on signals = –4.3%
Net return after payment of 7% in redemption fees = –11.3%
Abnormal return = 5.8% for six months
Mispricing of Mutual Funds 129
eight buy signals are followed by sell signals that do not meet the
thirty-day time limit. Thus, the redemption fee is payable in seven
cases. The gross return is –4.3 percent without accounting for the
redemption fees. Deducting a redemption fee of 7 percent for the
seven premature sales generates a net return of –11.3 percent.Again,
compared with the buy-and-hold return of –17.1 percent, an inves-
tor will earn an abnormal return of about 5.8 percent in a six-month
period, or an 11.6 percent annual abnormal return, by paying the
redemption fee each time it is less than the predicted return.
To conclude, it can be observed that mispriced mutual funds are
attractive for the smart investor. The redemption fees make the trad-
ing less attractive, but the returns from timing are still reasonable
and better than a buy-and-hold strategy. The returns can be im-
proved with a refinement in the regression model that includes
multiple index returns instead of just the S&P 500, as mentioned in
“The Trading Process.”
Using futures contracts can reduce the risk of trading. Since the trad-
ing strategies are designed to capture mispricing of mutual funds
and not market movements, it may be desirable to reduce market
risk. If the signal is based on the S&P 500, then at the time the inves-
tor buys the fund, he can also short-sell an equivalent number of
S&P 500 futures contracts. In this way, the investor is insulated
against any market movements related to the S&P 500. However,
the risk doesn’t fall to zero, as the fund will continue to have idio-
syncratic risk and the risk of any international markets that it is
exposed to. S&P 500 futures contracts are appropriate for domestic
and European funds, but Nikkei futures contracts are better suited
to Japanese and Pacific funds. The hedging can also be performed
by buying an inverse S&P fund such as Rydex Ursa instead of short-
selling S&P 500 futures contracts.
By taking an exactly opposite position in futures, the return of the
trading strategies can be improved by remaining fully invested. In
this case, the investor would be holding futures contracts when he is
not invested in the fund. Thus, when a sell signal occurs, the inves-
tor would sell the fund and buy S&P 500 futures contracts. When a
buy signal occurs, he would sell the futures contracts and buy the
fund. Since futures contracts do not need to be short-sold in this strat-
egy, the investor can flip between the mispriced fund and an S&P 500
index fund, instead of trading futures contracts.
Beyond the Random Walk130
Action Plan for Investors
The evidence and the trading strategies illustrate the widespread
mispricing of mutual funds. There are two alternatives open to
mutual fund investors: arbitrage and protection. Pursuing both al-
ternatives will reduce the mispricing of mutual funds.
ARBITRAGE THE MISPRICED MUTUAL FUNDS
The selection of mispriced mutual funds and execution of trading
strategies leads to abnormal profits. If more and more investors be-
gin to trade mispriced mutual funds, the mutual fund industry will
be forced to take these mispricings more seriously and adopt one or
more of the solutions highlighted in this chapter. Perhaps someone
might even design a more effective model to price mutual funds.
Whether you take advantage of the mispricings or not, you must
not allow others to take advantage of you. International funds, small-
cap funds, and many other funds are prone to timing by arbitrageurs.
Small investors should certainly not be holding any of the funds
listed in the tables here because these funds suffer from mispricing.
Investors should also examine the safeguards that their funds have
against frequent trading. Although investors may feel constrained
by redemption fees and similar features, these are good in the long
run because they limit the impact of mispriced NAVs. In addition,
investors should urge their fund managers to implement fair value
pricing in preference to imposition of redemption fees.
The evidence presented in this chapter and the trading strategy rec-
ommendations rely on past data. Since future market conditions
and market patterns may be completely different, there is no cer-
tainty that mispricing of mutual funds will continue in the future or
The trading strategies can easily become nonremunerative if the
fund families begin to properly price NAVs or if they impose oner-
ous restrictions on frequent trading. In particular, the funds listed
in the tables are likely to attract significantly more attention, and it
is very likely that investors will have to discover other funds that
Mispricing of Mutual Funds 131
• Net asset values for mutual funds are set at the end of each
day based on the last traded price. If the last trade occurs sev-
eral minutes or hours before the close of the market, the mu-
tual funds are likely to be mispriced.
• The mispricing problem is most severe for funds holding for-
eign stocks that stop trading several hours earlier. In addition,
many small-cap funds hold stocks that do not trade frequently,
and the NAV of these funds will also be based on stale prices.
Funds that have significant holdings of private equity, such as
venture capital funds, may have NAVs that are based on prices
several days or weeks old.
• Evidence points to the profitability of trading strategies. For
instance, foreign funds tend to have positive returns on days
following a rise in the S&P 500 index.
• The annual return from these trading strategies varies between
8.4 percent and 41.5 percent in spite of holding the foreign fund
only a quarter of the time. Moreover, the risk of these trading
strategies is less than the risk faced by a buy-and-hold inves-
tor. The risk of the trading strategies can be reduced further by
short-selling futures contracts.
• Transaction costs and restrictions on trading are a big concern.
However, there are many mutual funds that do not have re-
demption fees or loads. Fund supermarkets such as Schwab
can be used to avoid monitoring by mutual fund families.
• There are a few solutions to resolve the timing and mispricing
problem, but they are either inefficient or difficult to imple-
ment. Mutual funds impose redemption fees or use fair value
pricing to limit losses due to mispricing. Clearly, however, more
needs to be done.
• It is easy to set up a trading strategy to time the mispriced
mutual funds. First, find the mispriced mutual funds by re-
gressing the fund’s return on the previous day’s market re-
turn. Buy the mispriced fund whenever the market rises
abnormally, and sell otherwise.
• Investors should time mispriced mutual funds and ensure that
their own fund cannot be timed by other people. One hopes
the fund managers and the uninformed investors will wake
up and adopt solutions to eliminate or reduce mispricing.
Beyond the Random Walk132
The net asset values of mutual funds are mispriced when stale prices
are used for computation. Investors can make abnormal profits by
buying mispriced funds on days when the market rises abnormally
and selling them on subsequent days.
Historical Mutual Fund Price Data
http://www.qp2.com: Quotes-Plus has about fifteen thousand mutual funds in
its database. Nearly all of the equity funds reflect distributions in a timely
manner for the last four years. You also can see the distributions that have
actually been considered in its price series giving you added confidence.
Prices more than four years old are less likely to have been adjusted for
http://www.fasttrack.net: Fasttrack has about three thousand funds in its
database, selected on the basis of the funds’ popularity. Though the adjust-
ment for distributions is not perfect, it is probably the best in the industry. In
addition to prices, it provides extensive technical tools for detecting trends.
http://finance.yahoo.com: Inexpensive and easily accessible. However, this
and similar sites have two limitations. First, these sites do not accurately and
reliably adjust for all distributions, especially midyear distributions. Second,
these sites do not allow users to download data for multiple funds at the
http://www.vanguard.com: Reports distributions for Vanguard funds. Histori-
cal price data can be obtained from Yahoo! Distribution information for other
fund families can usually be obtained from their websites or by phone.
Current Mutual Fund Data
http://www.morningstar.com: Morningstar is the leader in information about
mutual funds. However, you must either have premium access to their site
or subscribe to Principia Pro for mutual funds on a CD. Principia Pro is
preferred over access to the website.
http://money.cnn.com: Excellent sites to obtain profiles of mutual funds—
category, assets held, and so on.
http://www.funds-sp.com: A competitor of Morningstar, Standard and Poor’s
also provides fund information.
Data About Index Returns
http://www.spglobal.com: Information about S&P 500. Unfortunately, no
historical return information is provided.
http://www.barra.com: Contains monthly returns for S&P 500, including
http://www.cme.com: Website of the Chicago Mercantile Exchange. The site
provides trading data for Nikkei futures and S&P 500 futures.
Mispricing of Mutual Funds 133
References for Further Reading
Bhargava, Rahul, and David Dubofsky. 2001. A Note on Fair Value Pricing of
Mutual Funds. Journal of Banking and Finance 25, 339–54.
Bhargava, Rahul, Ann Bose, and David Dubofsky. 1998. Exploiting International
Stock Market Correlations with Open-End International Mutual Funds. Jour-
nal of Business Finance and Accounting 25(5), 765–73.
Boudoukh, Jacob, Matthew Richardson, Marti Subrahmanyam, and Robert
Whitelaw. 2002. Stale Prices and Strategies for Trading Mutual Funds. Finan-
cial Analyst Journal 58(5): 87–97.
Chalmers, John, Roger Edelen, and Greg Kadlec. 2001. On the Perils of Financial
Intermediaries Setting Prices: The Mutual Fund Wild Card Option. Journal of
Finance 56(6), 2209–36.
Goetzmann, William, Zoran Ivkovic, and K. Geert Rouwenhorst. 2001. Day Trad-
ing International Mutual Funds: Evidence and Policy Solutions. Journal of Fi-
nancial and Quantitative Analysis 36(3), 287–309.
Zitzewitz, Eric. 2003. Who Cares About Shareholders? Arbitrage-Proofing Mu-
tual Funds. Journal of Law, Economics, and Organization, forthcoming.
1. Regression is a simple statistical technique available in common software
packages such as Microsoft Excel.
2. This chapter is based on the author’s analysis, and research by Bhargava and
Dubofsky (2001), Bhargava, Bose, and Dubofsky (1998), Goetzmann, Ivkovic,
and Rouwenhorst (2001), Zitzewitz (2003), Chalmers, Edelen, and Kadlec
(2001), Boudoukh et al. (2002), and Robert Whitelaw (personal communica-
tion). Many no-load funds with no transaction fees are available.
3. In row 11, the abnormal return is larger than the annual return in the previ-
ous column because the normal return for the thirty-four Pacific Asia funds
during that period was negative.
4. The figure 0.94 percent is not arbitrary but corresponds to the top 5 percent
of S&P 500 returns during the last two hours of trading.
5. Data Analysis is not part of the default installation of Excel. You must install
it separately after the default installation, or perform a custom installation
when installing Excel for the first time.
6. Most finance professionals use SAS, available from SAS Inc. However, SAS is
expensive unless your organization has a site license. SAS also has a steep
7. In addition, there are several domestic funds that have extremely high corre-
lations, almost 1.0. Upon closer inspection, it is discovered that the high cor-
relations occur for “fund of funds,” that is, funds that invest in other funds
that are otherwise inaccessible to individual investors. Since such funds must
wait for the net asset values of the funds that they hold, their own NAVs are
reported with a one-day delay. Once the data are corrected for delayed re-
porting, the high correlations for the domestic funds disappear, and no do-
mestic fund remains with a coefficient greater than 0.30 and R-squared > 10
Beyond the Random Walk134
Trading by insiders potentially conveys new information about the pros-
pects of a company. Insiders have far superior knowledge about the
company and the industry than the market. With this knowledge, their
predictions of future trends are likely to be more accurate than the pre-
dictions based on publicly available information. Therefore, mimicking
the trades of insiders generates above-normal annual returns of 10–15
To mimic insider trades, however, outsiders must first learn about
those trades. A change in the SEC reporting requirement makes the in-
formation relating to insider trades more current and more readily avail-
able. Since September 2002, insiders are required to report large trades
to the SEC within two business days. Earlier, insiders could have waited
as long as forty calendar days before reporting trades.
LEGAL AND ILLEGAL TRADES
Alleged insider trading by Martha Stewart made big news in 2002.1
is believed that she sold her holding of Imclone stock based on a tip
from the then CEO of Imclone. The tip came a day prior to public
disclosure of the FDA’s decision to delay approval of a drug applica-
tion submitted by Imclone. More than a decade ago, Ivan Boesky (see
Chapter 9, on merger arbitrage) was jailed for insider trading and
fined $100 million. Since the media focuses on illegal insider trading,
many investors mistakenly believe that all insider trading is illegal.
In reality, however, insider trading can be either legal or illegal.
Trading by Insiders
Trading by Insiders 135
Although the term “insider trading” connotes illegal trading to
some people, the focus of this chapter is on legal insider trading. For
ease of reference, in this chapter “insider trading” will always refer
to legal insider trading. Whenever the reference is to illegal trading,
“illegal insider trading” will be used. In addition, legal insider trad-
ing will also often be referred to as just “trading by insiders.”
Illegal insider trading refers to trading by insiders on the basis of
material and nonpublic information. Material nonpublic informa-
tion is any information that is likely to have an impact on the stock
price, such as information related to earnings, discovery of an oil
field, start of a Securities and Exchange Commission (SEC) investi-
gation, FDA approval or denial (as for Imclone), or a merger an-
nouncement. According to SEC regulations, such information must
be publicly disseminated, and insiders may not trade on that infor-
mation before it is made public. Besides officers and directors, for
the purpose of insider trading laws other individuals who have a
business relationship with the firm are also considered insiders.
Trading by outsiders (such as Martha Stewart’s trades in Imclone)
is also referred to as illegal insider trading when outsiders obtain
information from insiders who are aware of the potential impact of
that information. Thus, investment bankers (such as Ivan Boesky),
publishers of prospectuses, lawyers, and others, are subject to in-
sider trading regulations.
However, insiders (officers or directors of the firm) must be al-
lowed to trade. Insiders get company shares through the exercise of
stock options, through corporate awards, and through voluntary
purchase of those shares in the market. Consequently, a large fraction
of the insiders’ wealth can be tied up in the company’s stock. Insiders
will want to sell their holdings for two reasons. First, whenever large
expenses arise, such as the down payment for a home, they may want
to sell their company’s stock to raise funds. Second, insiders’ portfo-
lios are usually poorly diversified because of large holdings in a single
stock. Therefore, they may want to sell their company’s stock to in-
vest in other assets to diversify their portfolios.
SEC policies and regulations govern when and how insiders may
trade. Unlike the broad definition of an insider for illegal insider
trading, an insider is narrowly defined for legal trading. An insider
is the chairman, CEO, or president (top executive), a senior execu-
tive (or an officer), a member of the board of directors (director), an
owner of 10 percent or more of the firm’s shares (a large shareholder),
or a close relative of such persons. The key objective of the SEC regula-
information and do not speculate in their own stock. Besides the
Beyond the Random Walk136
threat of prosecution for illegal insider trading, insiders are required
to disgorge profits from offsetting trades (a buy and a sell) that oc-
cur within a six-month period when requested by either the SEC,
other stockholders, or the company. Insiders are also prohibited from
short-selling their own company’s stock.
In addition to federal laws, many companies have internal rules
that govern trading by insiders. First, insiders are not allowed to
trade within certain blocks of time: usually beginning as many as
thirty days before a scheduled or anticipated announcement and
until one to two weeks after that announcement. Announcements
include earnings, mergers, discoveries, and so on. Second, in many
cases, insiders must seek approval of the company’s compliance
officer prior to trading in the company’s stock and sometimes even
for any trading in the insider’s entire securities portfolio.
INFORMATIVENESS OF TRADES
Under SEC regulations, insiders must report all trades to the SEC
soon after they occur. Every year there are more than two hundred
thousand trades by insiders reported to the SEC. What do these
trades mean, and do they contain information that can be gainfully
used by investors? The short answer is “yes.”
Insiders, especially the top management, have a much better sense
of how the company is doing and expected to do in the future than
the market. As a matter of fact, the market gets a lot of its informa-
tion about a company from the company itself. And the company
routinely shares that information with the market. For example, the
management discusses the company’s future prospects at the time
of an earnings announcement. Many corporate events also convey
information about the management’s beliefs about the true value of
the company. Dividend increases, stock repurchases, and debt is-
sues are usually interpreted as positive events. Dividend decreases
and new stock issues are interpreted as negative events. At other
times the management may voluntarily share information with the
market. However, any voluntary sharing of positive information is
usually discounted by the market unless the company is very selec-
tive about making such pronouncements.
It is important to note that insiders’ knowledge of the company
is usually superior to that of the market. Though insiders cannot
trade on the basis of material information, they can trade in the nor-
mal course of firm operations. Insiders may have the same detail of
information as external participants but interpret that information
Trading by Insiders 137
differently. Their interpretation, due to their expertise and knowl-
edge, is considered to be superior to that of an external analyst. For
example, it is common knowledge that the steel industry is fighting
for survival. However, does it mean that the industry will die in
five years, ten years, twenty years, or never? The opinion of the
CEO of a steel company is probably more valuable than the opinion
of anyone else. How do the insiders share that information? Their
trading conveys that information in a credible way because insid-
ers stand to lose or gain from their trades. Thus, trading by insiders
has the potential to convey new information to the market.
EVALUATING INSIDER TRADES
Since there are hundreds of thousands of trades by insiders every
year, how does one evaluate so many of them? And do they all con-
tain useful information? In fact, there are many insider purchases
and insider sales that contain no information. Sometimes insider
buying is involuntary. For example, a new member of management
may be required to purchase a hundred thousand shares of the com-
pany to align his or her personal incentives with those of the stock-
holders. Stock options are a popular form of compensation. When
an insider exercises a call option (an option to buy stock at a prede-
termined price), he or she automatically acquires shares of a com-
pany. Many insiders will immediately sell the acquired shares so that
their assets do not become even more concentrated in one stock. Typi-
cally, insiders exercise their options when they need to raise funds. A
CEO may exercise his or her stock options, automatically receive one
million shares, and sell them immediately in the open market. In ad-
dition to using options, insiders may liquidate part of their stock hold-
ings to meet major expenses.
Besides the need to eliminate trades with no information, it is
also necessary to distinguish among trades based on the amount of
information. Do larger trades have greater predictability? Does com-
pany size make a difference? Is there a difference between insider
selling and insider buying?
Evaluation of insider trades is not easy. The past performance of
newsletters specializing in reading and interpreting trades of insid-
ers has not been spectacular.2
In fact, two newsletters followed by
Hulbert Financial Digest underperformed the broader market though
they pursued riskier strategies. Insiders’Portfolio gained 118.9 percent
from January 1985 to June 1992, compared with a gain of 197.6 per-
cent by the broader market, and Market Logic earned 339.2 percent
Beyond the Random Walk138
from July 1980 to June 1992, compared with a gain of 432.7 percent
for the Wilshire 5000. Neither of these letters exist any longer. In
addition, Inside Track, Insider Chronicle, and Insider Scores have dis-
continued publication. The performance of one current newsletter
is slightly better, with a return of 11.2 percent annually compared
with 10.5 percent for the broader market. For details, see “Newslet-
ters Based on Trading by Insiders” later in this chapter.
The past existence of many newsletters on insider trading sug-
gests that market watchers consider those trades to be important.
However, the performance of market pundits in analyzing trades
suggests the need for a more careful analysis of what works and
what doesn’t, and how to more carefully interpret the data that are
revealed by insiders. That is the purpose of the next section, which
summarizes evidence related to how insider trading can predict
future market returns.
The evidence presented is based on data obtained from the Securi-
ties and Exchange Commission’s Ownership Reporting System.
However, the data can also be easily obtained from secondary
sources (see “Internet References”). Since only open market trades
of insiders contain information, private trades and trades with the
company are excluded from consideration.
In a moment you will observe that insider selling is almost four
times as large as insider buying. The main reason for the difference
is that insiders have a large number of shares that are not acquired
through open market buying, whereas all of their sales are in the
open market. Although sales convey valuable information, it is the
purchases by insiders that are more interesting and informative.
It is also important to define a metric for measuring the size of
insider buying or selling. There are several ways of aggregating the
numerous trades by insiders in a given month for a single com-
pany. Trading by insiders could be counted based on the net num-
ber of shares traded (buys minus sells), net number of transactions,
net number of insiders (buyers minus sellers), and so on. Although
the net number of insiders is important, the most effective way is to
use the net number of shares traded. Accordingly, the results pre-
sented in the next two subsections are based on the net number of
shares traded as the measure of insider trading.
Trading by Insiders 139
The following evidence is based on an analysis of insider trades by
major studies over a twenty-year period (1975–94) and a twenty-
one-year period (1975–95). First, the results show that if insiders
buy in one month, there is a 38 percent chance that they will buy in
the following month and only an 11 percent chance that they will
sell. A similar pattern exists for insider sales. This implies that in-
siders do not make all of their trades right away but do it slowly
over a period of several months. One reason for splitting trades may
be to minimize the price impact of trades by not alerting the media
or other investors to their beliefs about the company. This is a com-
mon practice among large traders whenever trades are based on
information: large orders are split into small orders spread over
many trading days. The implication of this type of serial buying or
serial selling is that the opportunities to trade do not disappear im-
mediately, and so outsiders may be able to pattern their own trades
using information from insider trades.
Second, a firm is likely to perform better following an insider
buying month than an insider selling month. The difference in re-
turns over the subsequent twelve-month period varies from 4.8 per-
cent to 18.7 percent, as shown in Table 7.1.
Overall, it can be seen that stocks of firms where insiders have
been actively buying outperform stocks where insiders have been
actively selling. If one month’s insider trades are used to signal a buy
or a sell, stocks with net buys earn 24.0 percent, whereas stocks with
net sells earn 15.1 percent in the subsequent twelve-month period.
The performance improves if a three-month period for estimation is
Table 7.1. Returns Following Insider Activity (in percent)
12-month return 12-month return
12-month adjusted 12-month adjusted 12-month
return for market return for market return
Buys 24.0 4.5 29.6 7.5 30.5
Sells 15.1 –2.7 10.9 –6.1 9.5
Estimation period = 1 month.
Estimation period = 3 consecutive months with the same signal.
Estimation period = 12 consecutive months with the same signal.
Beyond the Random Walk140
chosen with the additional condition that each of the three months
must be of the same sign (all three net buys or all three net sells).
Adjusted for the market, measured as the equally weighted return
on all stocks, a strategy of buying stocks with a history of three-
month net buys by insiders earns a return of 7.5 percent more than
the market, whereas a strategy of buying stocks with a history of
sells would earn 6.1 percent less than the market. Extending the
estimation period to twelve months of nonconflicting net buys or
net sells results in a difference of 21 percent over the subsequent
year. Clearly, the trading pattern of insiders is a useful indicator of
future returns for the company.
Third, insiders seem to time their purchases and sales. If an in-
sider wants to buy but thinks (or knows) that the stock is likely to
fall in value, he will wait for the stock to fall before buying. Simi-
larly, if an insider wants to sell but expects the stock to rise, he will
wait before selling. The evidence indicates that the probability of
selling by top executives increases to 69 percent if the stock has risen
more than 10 percent in the last six months. On the other hand, the
probability of selling is only 52 percent if the stock has fallen more
than 10 percent in the last six months. Does this really indicate that
insiders know what is going to happen to the stock, or is it simply
that their price targets for trading have been met? Combined with
the continuity in trading patterns and continuity in return patterns
enumerated above, it seems that insiders do have the ability to time
Finally, if all insider trades are aggregated, they may provide some
information about future economic growth. If insiders can provide
information about their respective companies, then it seems rea-
sonable that if all of those signals are consolidated, insiders may be
able to predict the direction of the economy and the overall stock
market. Indeed, that is true.
Table 7.2 is constructed by counting the number of firms with net
insider buys and net insider sells during each of the estimation pe-
riods. A buy signal is issued if more than 50 percent of the firms
have net insider buys, and a sell signal is issued if more than 50
percent of the firms have net insider sells. If trade signals are based
on a three-month estimation period, then the return in the subse-
quent three-month period is 5.7 percent following buys and 3.9 per-
cent following sells. The difference of 1.8 percent is equivalent to an
annualized return of 7.2 percent. The prediction of future growth
improves if longer estimation and holding periods are used. With a
twelve-month estimation period and a six-month holding period,
Trading by Insiders 141
the difference in returns following buys and sells is 7.9 percent, which
translates into an annualized return of 15.8 percent. That is a big
difference. The probability of an up market is 80 percent for buys
compared with 65.2 percent for sells.
The newsletter, Vickers Weekly Insider, uses aggregate trading by
insiders to predict the direction of the market. It computes a sell-
buy ratio based on insiders’ trades, and claims that if the ratio is
less than 2.00, the market is likely to rise, and if the ratio is greater
than 2.50, the market is likely to fall. Note that 2.00 and 2.50 are
used as cutoffs because there is significantly more insider selling
than insider buying.
Some anecdotal evidence related to trading by insiders is illus-
trative. Until May 2000, insiders at Lucent Technologies were ac-
tively selling their stock at prices in the range of $40–70. Thereafter,
there were relatively few trades by insiders. In August 2002 insid-
ers became active once again. This time, the CEO and several direc-
tors were actively buying Lucent stock at a price of less than $2.00.
REFINING THE RESULTS
In addition to the broad evidence presented, there are a variety of
characteristics of insider trades that can help refine and improve
the predictability of stock returns for the insider’s firm. In particu-
lar, the identity of traders, number of shares, firm size, type of trade
(buy or sell), and consensus among insiders are factors that can sig-
nificantly improve the results.
Identity of Insiders
It is reasonable to expect that top executives (chief executive officer,
chief financial officer, and chief operating officer) will know the firm
more intimately than anyone else in the organization. Other mem-
bers of the senior management team may be well informed about
Table 7.2 Determining Buy Signals Based on Insider Activity (in percent)
Estimation period 3 months Estimation period: 12 months
Holding period: 3 months Holding period: 6 months
Adjusted of an up Adjusted of an up
return market return market
Buys 5.7 74.2 14.1 80.0
Sells 3.9 62.5 6.2 65.2
Beyond the Random Walk142
their particular area but not necessarily about the whole organiza-
tion. The board of directors provides overall direction to the com-
pany but is essentially given information by the top executives.
Moreover, the board usually meets only a few times a year, so its
access to information is somewhat limited. Large shareholders are
outsiders and are not privy to any information unless they have
representation on the board of directors.
The predictive power of insider trades is related to the amount of
information the insiders have. The following table shows the per-
centage of average abnormal returns earned during the twelve months
following insider purchases (or insider sales). Evidence indicates that
it is best to ignore trades of large shareholders and pay close atten-
tion to trades of other insiders, especially the top executives.
Top executives 5.0
Large shareholders 0.7
Number of Shares Traded
It is natural to expect that larger trades will be more informative
because insiders will trade more if they are more confident about
their assessment. Small trades, on the other hand, will convey little
information. The results are reported below by size (%) of the trade:
1–100 shares 0.8
101–1,000 shares 2.9
1,001–10,000 shares 4.0
10,001–20,000 shares 4.1
20,001–100,000 shares 4.8
100,001–1,000,000 shares 3.8
More than 1,000,000 shares 0.5
The evidence supports the expectation that larger trades are infor-
mative. However, once the number of shares traded becomes very
large, the trades don’t remain as informative. There are probably
two reasons for this decline. First, large trades are likely to be scru-
tinized by the media and the SEC. Therefore, an insider will avoid
large trades based on private information and will make large trades
only when they are triggered for other reasons, such as a tax pay-
ment that can neither be avoided nor delayed. As mentioned above,
large informative trades are usually split into slightly smaller trades.
Trading by Insiders 143
Second, large trades are more likely to be sales than purchases. As
you will see momentarily, sales have lower predictability than pur-
chases. Therefore, large trades tend to contain less information.
Firm size can be an important factor in the predictive ability of insid-
ers for several reasons. First, larger firms have many stock analysts
who continually study and report on the firm. As a result, insiders’
evaluation of the firm may not be as important as in the case of a
smaller firm where no outsiders are actively producing and dissemi-
nating information about the firm. Second, any particular event is
likely to have a much larger impact on a smaller company than on a
larger firm. A new marketing relationship with AOL Time Warner
will be more valuable to Flowers.com than to Amazon.com because
Amazon.com is a much larger company with many established chan-
nels for selling. Consequently, the same piece of information may
elicit a significantly larger price response from Flowers.com stock than
from Amazon.com stock. Or, as in the case of Imclone, denial of ap-
proval of one drug by the FDA caused the stock price to plummet by
75 percent. The data below confirm the predictive ability of insider
trading based on firm size.
All insiders Officers only Top executives only
Size (%) (%) (%)
<$25 million 6.2 7.0 7.8
$25–100 million 3.1 3.4 4.0
$100–1,000 million 2.3 2.5 2.9
>$1,000 million 1.7 2.0 3.9
The twelve-month market-adjusted return is much higher for
smaller firms than for larger firms. The table also shows that trades
by top executives can predict the future more accurately than trades
by other insiders. If the size of trades is combined with firm size
and the identity of insiders, the results are more promising. The
twelve-month market-adjusted return following large trades (more
than ten thousand shares) by top executives in firms with a market
capitalization of less than $25 million is 9.8 percent, much higher
than the 3.7 percent return for firms with a market capitalization of
more than $1,000 million.
Purchases Versus Sales
On average, selling by insiders is nearly four times as large as buy-
ing by insiders. Moreover, selling is more likely to be involuntary,
Beyond the Random Walk144
due to liquidity or diversification needs, whereas buying is more
likely to be voluntary, for speculative reasons. Consequently, buy-
ing by insiders should be more significant than selling by insiders.
The twelve-month return following trades by top executives is 8.9
percent for buys and –5.4 percent for sells (avoidance of a loss). For
small firms and top executives, the twelve-month profits (or losses
avoided for sales) are as follows:
All insiders Officers Top executives
Buys 10.4% 11.9% 12.3%
Sells –0.8% –0.9% –2.8%
The difference between purchases and sales is smaller but sig-
nificant even for larger firms. Since selling is more common, it is
natural to expect that a high level of sales is less abnormal than a
comparable high level of purchases. Moreover, insiders may choose
not to buy more stock even if they have positive information about
the company, for two reasons. First, almost all purchases, except those
made by new insiders, are likely to be based on special information
and, therefore, subject to closer scrutiny. Second, purchasing addi-
tional shares of a company where the insider is already heavily in-
vested increases his risk significantly. Therefore, insiders with positive
information may choose not to sell instead of buying more shares.
Thus, the absence of sales and purchases is also a strong signal of
positive information, especially if the top executives are inactive.
Number of Insiders
Finally, the number of insiders who buy or sell can sharpen the in-
formativeness of trades. If only one insider is selling, then that may
simply be due to his personal situation. However, if several insid-
ers are selling, it is easier to claim that the selling contains new in-
formation. The evidence supports this notion. If only one insider is
selling, then the twelve-month abnormal return is 1.2 percent, which
improves to 4.6 percent if three or more insiders are selling. On the
other hand, insider buying is rare enough that even following the
purchases of one insider will generate an abnormal return of 4.2
percent, which improves slightly to 4.7 percent with three or more
Overall, the evidence suggests that:
• Top executives know more.
• Large trades (up to 500,000 shares) reveal more.
Trading by Insiders 145
• Purchases have better predictive ability.
• Consensus among insiders is important.
• It is easier to forecast returns for smaller firms than for larger
Note, however, that the evidence presented does not account for
transaction costs. Since those costs are high for small firms, and
sometimes prohibitively high, it may be necessary to alter the above
recommendations for implementation of a trading strategy.
Though it is important to keep the practicability of a trading strat-
egy in mind, evidence reveals that copying the large trades (more
than 10,000 shares) of top executives is profitable. Outsiders can
mimic these trades and earn a return of 7 percent for purchases and
4.9 percent for sales over a twelve-month period after adjusting for
the market and accounting for transaction costs.
If all trades (large and small) based on a six-month period are
considered, the insider purchases outperform insider sales by 7.8
percent over the next twelve-month period. Adjustment for risk re-
duces the overperformance to 4.8 percent.
RESULTS BASED ON THE WALL STREET JOURNAL’S
INSIDER TRADING SPOTLIGHT
Realizing the importance of insider trading to investors, the Wall
Street Journal began publishing an “Insider Trading Spotlight” col-
umn in 1988. The column reports the top ten insider sales and the
top insider purchases by dollar value reported to the SEC. Until
early 2003, the column appeared weekly, but now it appears daily.
The column is also available online. In addition to reporting the
insiders with the largest buys and sells, the online version also re-
ports companies with the most insider buying or selling activity.
Similar information is also published by Barron’s and several
Internet sites such as Quicken and MSN Money. The availability of
insider trading data is listed in “Internet References.”
A few studies have examined whether trading based on top ten
insider buys and sells is profitable or not. The research finds that on
the day of publication there is an abnormal increase in the prices of
stocks that had large insider buys and an abnormal decrease in the
prices of stocks with large insider sells. The price change is about 1
percent, statistically significant, and accompanied by significantly
higher volume. If only insider buys are considered, then the mar-
ket-adjusted return on publication day is about 2 percent, but the
cumulative market-adjusted return for a one-year period is small.
Beyond the Random Walk146
Because the data can be compiled independently without waiting
for the print edition of the Wall Street Journal, this insider trading
activity suggests a possible trading strategy. However, the above
returns do not account for transaction costs, which can cut into the
profitability of a trading strategy.
The evidence indicates that trading by insiders reveals information
about future stock price movements. Outsiders can benefit by ob-
serving and mimicking the insider trades. Among the two hundred
thousand trades by insiders every year, large (but not too large)
purchases by top executives, especially of small companies, are most
informative. However, even trades publicized in the news media
can be profitable and informative for investors.
Besides constructing a trading strategy based on trades by insid-
ers, investors can use that information to reconfirm planned buys
and sells. For example, if an investor is thinking of buying Pepsi
stock but insiders are selling, then it may not be the best time to
invest in that stock. Similarly, if an investor needs to liquidate some
stocks to meet certain expenses, he should look at the trades by in-
siders and not sell the stocks that insiders have been buying.
Change in Reporting Requirements
The evidence presented above is based on SEC reporting requirements
and data in secondary sources such as newspapers, magazines, and
the Internet. However, recent SEC reporting changes accelerate re-
lease of insider trading information to the public and will probably
improve outsiders’ gains. The changes are discussed below.
Until August 2002, insiders had until the tenth day of the follow-
ing month to report open-market trades, which meant that trades
could be reported as many as forty calendar days after they occurred.
For shares sold back to the company, insiders could wait to report
until forty-five days after the start of the next fiscal year. However,
in accordance with new SEC regulations, insiders are now required
to report their large trades, typically the ones of interest to inves-
tors, within two business days. All other trades must be reported
by the second business day of the following week. This is a signifi-
cant change from the earlier regulation, under which the average delay
in reporting was about twenty-seven calendar days and could be even
Trading by Insiders 147
Moreover, insiders must now file their reports electronically and
post them on the company’s website. Under the old regulations,
insiders were required to file trades by the deadlines mentioned
earlier. However, electronic filing was not required. As most of in-
sider trading filings were on paper, there was an even greater delay
before the filings were transcribed and entered into SEC’s EDGAR
Finally, as mentioned above, the Wall Street Journal’s “Insider Trad-
ing Spotlight” column can be accessed online before it appears in
While not entirely clear, the reasons for persistence of insider trad-
ing strategies are probably related to a lack of understanding and a
lack of interest. There are few hedge funds, if any, that specialize in
insider trading. It is possible that professional arbitrageurs are more
attracted to strategies that are less uncertain and those that require
a shorter holding period. Many other people seem to lack a com-
plete understanding of insider trading. Newsletters devoted to strat-
egies based on insider trading have not been particularly successful
and have a low survival rate. The reason for their failure is most
likely a lack of understanding. Many individual investors avoid any
strategies related to insider trading because they mistakenly believe
that all insider trading is illegal. Nejat Seyhun’s book on insider
trading, while a brilliant piece of work by an expert in the field, was
largely inaccessible to the small, individual investor.
The changes in reporting mentioned in the previous section will
definitely make trades by insiders more transparent and timely. Con-
sequently, the evidence presented above and the results presented
below will improve and become more rewarding to the investors. It
is also anticipated that more investors will begin to construct strat-
egies related to insider trading.
The Trading Process
There are two ways investors can use information related to trad-
ing by insiders: on an individual stock level or on an aggregate in-
dustry or market level. At an individual stock level, investors can
use the data either to set up trading strategies or to alter trading
Beyond the Random Walk148
behavior (for example, not buying an individual stock when insiders
are selling it). The use of data on insider trading for predicting broad
market movements and for altering individual trades is discussed in
“Other Uses and Refinements of Insider Trading Information.”
Institutions have access to large databases to screen stocks and
identify those that may be of interest. However, the situation for
individual investors is different. Unlike stock and mutual fund da-
tabases, which are freely available and easily accessible, databases
that contain insider trading data are too expensive and generally
inaccessible to individual investors.
There are a few sources [such as the Wall Street Journal, Vickers
Stock Research (vickers-stock.com), and Thomson Financial Net-
work (thomsonfn.com)] that provide information about stocks and
insiders with very high levels of insider trading activity. This infor-
mation is freely accessible to individual investors. However, the in-
formation in these sources is already prescreened and by their own
criteria, not necessarily the criteria established based on the evi-
dence presented in “Evidence” and “Change in Reporting Require-
ments,” above. Therefore, the list of stocks obtained from these
sources must be screened once again based on the criteria discussed
above and enumerated in the following steps.
Step 1: Obtain a list of stocks for review from one or more of the
sources in “Information on Trades by Insiders for Individual Stocks.”
Step 2: Get insider trading data for each of the stocks from
Quicken.com. In case any information is suspect, it can be verified
with Vickers. Select transactions during the previous six months.
The process can also be repeated by considering transactions only
during the last three months.
Step 3: Exclude transactions that fall into the following categories:
• Trades by large outside shareholders, those who own more than
10 percent of the stock
• Individual transactions that are larger than 500,000 shares
• Individual transactions that are smaller than 101 shares
• Private trades, where no market transaction takes place
• Sales less than or equal to the exercise of options on the same
• Planned sales reported on Form 144
• Initial trades reported on Form 3 and annual ownership on
Trading by Insiders 149
Trading by insiders is reported to the SEC on four different forms.
For the purpose of this chapter, Form 4 is the only relevant form. It
is used to report trades of existing insiders to the SEC. Form 144
alerts the SEC to planned sales of restricted securities or securities
held by an affiliate of the issuer; it is irrelevant because restricted
securities are not of much interest to individual investors. Form 3 is
the initial transaction by an insider after becoming an insider; ini-
tial purchases by an insider are usually required by the company
and therefore are involuntary. And Form 5, the annual statement of
ownership by insiders, contains no new information.
Step 4: Sum up the total number of shares sold and the total num-
ber of shares purchased. Compute the sales-to-purchase ratio (SP),
provided the number of shares purchased is not zero.
Step 5: Repeat step 4 but use the number of unique insiders in-
stead of the number of shares. Again compute the ratio of the num-
ber of unique insiders selling to the number of unique insiders
buying (SIPI), provided the number of unique insiders buying is
Step 6: If SIPI and SP (calculated in steps 4 and 5) are dissimilar—
say, different by more than 50 percent—then explore the reasons for
the dissimilarity. If a single insider is making up the bulk of the
purchases or sales, then the SIPI and SP are likely to be quite differ-
ent. In such a case, one should rely more on SIPI than on SP, or
should exclude that insider from all computations. For example,
Bill Gates sold $1.1 billion worth of Microsoft stock in the first six
months of 2002. Since no insider is likely to buy such a large quan-
tity of Microsoft stock, are Bill Gates’ sales a bearish signal? If you
consider the past sales by Bill Gates, he sold $1.25 billion in the first
six months of 2001 and another $1.25 billion in the second six months
of 2001, it is obvious that the sale of $1.1 billion in the first six months
of 2002 is unlikely to convey much information. So it may be best to
exclude Bill Gates from computation of sales and purchases of
In any case, if no reasons can be discovered for an unusually large
trade by an insider, go to step 7, which contains recommendations
Step 7: A buy is recommended under any one or more of the fol-
• There is no selling by insiders over the observation period (at
least six months).
• If there is selling by insiders, then SIPI and SP are both less
than 1, and the net number of insiders buying is at least 3.
Beyond the Random Walk150
A sell is recommended if the net number of insiders selling is at
least three and SIPI and SP are at least 2.00. The remaining stocks
The trading process outlined above is applied to all stocks featured
in the weekly “Insider Trading Spotlight” column of the Wall Street
Journal (WSJ) during December 2001. The WSJ is selected because it
is easily accessible to all investors. However, WSJ reports the larg-
est trades by insider, not by company. Thus the same report may
contain several insiders from the same company.
In December 2001 “Insider Trading Spotlight” appeared in the
WSJ four times, each time listing the ten largest insider sales and
the ten largest insider purchases. The total of forty insider purchases
and forty insider sales represented sixty different companies. Using
the steps in the trading process for each of these companies, the
results are reported in Table 7.3. Firm size and the number of shares
are as of the end of December 2001. The shares sold or bought and
the insiders selling or buying are based on the July-December 2001
period. The SP and SIPI ratios are reported in the second and third
last columns. Whenever the number of shares purchased is zero or
the number of insiders buying is zero, the ratios cannot be calcu-
lated. In those cases, the ratios are indicated to be “high” (greater
In some instances there is no insider trade that qualifies for inclu-
sion based on the criteria set out earlier. How can that be reconciled
with the fact that the company was featured in the WSJ based on
the size of trades? Typically, it means that the trade reported in the
WSJ was related to the exercise of options. While sales related to an
option exercise may have some information, the evidence indicates
that the predictability of sales concurrent with an option exercise is
close to zero. Hence all such trades are excluded. As a result, some
companies have zero sales and zero purchases. When both sales
and purchases are zero, the ratios are again undefined but indicated
to be “low.” Since the norm for a company’s insiders is to be selling
company stock, zero sales suggest a buying opportunity.
The last column in Table 7.3 has the recommendations based on
step 7: fifteen sells and twenty-six buys. The stock returns for these
recommendations are presented in Table 7.4. Of the fifteen stocks
recommended as a sell, only two stocks earn a positive return in the
following six-month period, January-June 2002. Overall, the fifteen
Table 7.3 Trading by Insiders of Firms Highlighted in the Wall Street Journal
Firms are taken from the “Insider Trading Spotlight” column of the Wall Street Journal during December 2001. Firm size and number of shares
are as of the end of December 2001. Insider transactions are based on the July–December 2001 period. The last row has trading recommen-
dations, where S is a sell and B is a buy. A — indicates that no trading recommendation can be made based on insider trading.
Ratio of Selling to
Firm Number Shares Shares Sales to Insiders Trading
Ticker Size of Shares Sold Bought Insiders Insiders Purchases Buying Recom-
Symbol (millions) (millions) (thousands) (thousands) Selling Buying (SP) (SIPI) mendation
ADP 36,000 617 346 0 11 0 high high S
AHC 5,500 89 0 12 0 1 0 0 B
AMHC 460 14 151 0 6 0 high high S
APD 10,650 227 0 0 0 0 low low B
ATVI 1,350 52 135 0 2 0 high high —
AXR 40 7 0 555 0 1 0 0 B
BEN 9,200 261 234 0 12 0 high high S
BLS 71,600 1,877 0 0 0 0 low low B
BRCM 7,600 186 1,881 0 9 0 high high S
CAH 29,200 451 275 0 3 0 high high S
CB 11,700 170 2 10 1 1 0.2 1 —
CEC 1,210 28 0 30 0 1 0 0 B
CEFT 16,500 504 309 0 6 0 high high S
CLSR 315 13 87 3 4 1 29 4 S
COT 1,100 68 555 0 12 0 high high S
CSGS 2,150 53 810 50 4 1 16 4 S
DBRN 460 18 0 0 0 0 low low B
DCGN 525 54 94 0 1 0 high high —
DELL 70,900 2,607 1,970 0 7 0 high high S
DIAN 450 7 100 0 1 0 high high —
ESV 3,350 135 4 65 1 1 0.1 1 —
(continues on next page)
Table 7.3 Trading by Insiders of Firms Highlighted in the Wall Street Journal (continued)
Ratio of Selling to
Firm Number Shares Shares Sales to Insiders Trading
Ticker Size of Shares Sold Bought Insiders Insiders Purchases Buying Recom-
Symbol (millions) (millions) (thousands) (thousands) Selling Buying (SP) (SIPI) mendation
FCBP 100 5 0 79 0 1 0 0 B
GNSS 2,050 31 450 9 12 1 50 12 S
GR 2,700 102 0 227 0 9 0 0 B
HCP 2,000 56 50 0 1 0 high high —
HIG 15,000 238 300 19 1 3 15 0.3 —
HMA 4,500 242 0 2 0 1 0 0 B
HU 1,325 46 17 40 2 6 0.4 0.3 B
IBM 20,8000 1,723 71 5 3 1 14 3 —
ITT 4,625 92 0 0 0 0 low low B
JAKK 350 18 260 0 3 0 high high S
KG 10,300 246 267 2 2 2 high 1 —
KIND 900 17 400 0 1 0 high high —
MBBC 50 3 0 141 0 10 0 0 B
MBFI 190 7 0 21 0 2 0 0 B
MMC 29,500 275 0 0 0 0 low low B
MOBE 19 15 0 97 0 4 0 0 B
MPH 240 15 950 37 5 2 26 2.5 S
OGLE 80 5 0 82 0 8 0 0 B
OPTN 300 16 450 0 1 0 high high —
OVER 2,000 57 865 0 10 0 high high S
PMSI 75 16 0 105 0 4 0 0 B
PPDI 1,675 52 25 150 1 1 0.2 1 —
PZZA 625 23 0 0 0 0 low low B
RYL 970 13 9 0 2 0 high high —
SRNA 875 40 400 0 1 0 high high —
STOR 600 97 1,325 0 8 0 high high S
STZ 1,600 37 0 0 0 0 low low B
SYMC 4,600 70 8 0 7 0 high high —
TDSC 185 13 0 141 0 1 0 0 B
THC 19,000 325 0 10 0 1 0 0 B
THER 1,000 39 0 91 0 4 0 0 B
TMPW 4,500 106 793 31 5 8 26 5 —
TRGL 30 6 0 208 0 3 0 0 B
TRKN 165 14 0 0 0 0 low low B
TW 1,660 85 2 203 1 1 0 1 —
VTA 275 35 0 146 0 6 0 0 B
WMB 13,100 515 13 46 1 2 0.3 0.5 —
WSBI 100 5 0 4 0 1 0 0 B
WYN 100 168 408 0 1 0 high high —
Trading by Insiders 155
stocks lose an average of 28.6 percent, compared with a loss of 13.8
percent for the S&P 500. Thus, the net S&P 500 adjusted return is
–14.8 percent for the six-month period, or an annualized return of
–29.6 percent. The results for shorter periods are similar, suggesting
that stocks that are aggressively sold by insiders underperform the
market in subsequent months.
In contrast to the abnormal fall in prices for stocks with sell rec-
ommendations, stocks with buy recommendations outperform the
market. Out of the twenty-six stocks with a buy, only nine stocks
experience a fall in prices in the next six months. The overall return
is 15.0 percent, compared with the S&P 500’s return of –13.8 per-
cent. Thus, stocks with a buy recommendation earn a whopping
28.8 percent abnormal return over a six-month period, or an annu-
alized abnormal return of 57.6 percent! Similarly, the one-month
abnormal return is 4.6 percent and the three-month abnormal re-
turn is 10.7 percent.
The large magnitude of returns following sells (–29.6 percent an-
nualized) and buys (57.6 percent annualized) is surprising. Trans-
action costs will lower the returns by only about 1 percent over a
six-month period. So, what can explain the large returns to insider
Figure 7.1 Returns to buy and sell recommendations based on insider trades are
shown. The S&P 500 return is provided for comparison. The insider trades are taken
from the “Insider Trading Spotlight” columns that appeared in the Wall Street Jour-
nal during December 2001. The trading strategies are implemented from January
2002 to June 2002.
Informativeness of Insider Trades
Buys Sells S&P 500 Return
Beyond the Random Walk156
trading in this analysis? Perhaps the sample size is too small, with
only sixty firms and trading recommendations for only forty-one
firms. It is also possible that insiders can predict their own company’s
performance in absolute terms rather than in relative terms. That is,
they can predict what might happen to their stock price independent
of market movements. Indeed, the average increase in the stock price
following buys was only 15 percent. If the broader market had also
risen during the same period, then the insider buys would not have
generated the large abnormal profits witnessed. Nonetheless, it is
sufficient to state that these abnormal returns are large and attractive.
Other Uses and Refinements
of Insider Trading Information
Besides a trading strategy for individual stocks discussed above, in-
sider trading information can be used in at least two other ways. First,
the information provided by insiders can be used to alter the timing
of trades. As far as possible, outsiders should mimic the trades of
insiders. If insiders are selling a stock aggressively, it does not seem
reasonable to buy the same stock. Similarly, do not sell while insid-
ers are postponing sales. An investor can follow steps 2 through 7 of
the trading process for each stock he wants to trade. If the recom-
mendation based on step 7 agrees with his desired action, then he
should follow through. Otherwise, he should wait.
The second use of insider information is in trying to predict future
direction of the broader market. If insiders can accurately predict how
their company is likely to perform, then an aggregation of all insider
recommendations should suggest whether the overall market or an
industry is a buy, sell, or hold. The Vickers weekly insider report (go
to vickers-stock.com) computes an “Insider Index” based on insider
trading among all companies that is supposed to predict market di-
rection. Similarly, Thomson provides its assessment of the market
through its “Market Tearsheet” (go to insider.thomsonfn.com). The
third source is WallStreetCity (go to www.wallstreetcity.com), which
lists insider trading by industry. While these indices may be useful,
the construction of the indices is critical. Detailed information on
the construction of these indices is not available, and it is unclear
whether these indices follow the criteria described above. However,
for individuals and institutions with access to insider trading data-
bases, it may be possible to construct an index that can accurately
predict future market movements based on insider trades.
Trading by Insiders 157
The results reported above in “Strategy Implementation,” based on
broad analysis, are fairly good. However, analysts and newsletter
pundits have attempted to further refine the analysis to improve
the returns. Although the refinements discussed below have intui-
tive appeal, there is no empirical evidence to either support or re-
fute the value added by these refinements.
The first refinement is based on the fact that different insiders
may have different levels of predictability. An insider may repeat-
edly sell before the stock falls, or buy before the stock rises. A sec-
ond insider’s trades, on the other hand, may have no predictive
power. So, past performances of insiders can be used to weight in-
sider trades, with the first insider’s trades getting a significantly
higher weight than the second insider’s trades.
The second refinement would use deviations from normal sell-
ing and buying patterns to make trading recommendations instead
of using the absolute value of net insider sales. For example, sup-
pose Bill Gates has established a normal pattern of liquidating $1,250
million worth of Microsoft stock every six months, but he sells only
$100 million in the current six-month period. Is this a buying op-
portunity, or should you sell Microsoft stock? Looking at the abso-
lute number of insider sales of $100 million, it may be prudent to
sell. However, compared to the normal selling activity of $1,250
million, a $100 million sale might suggest a buy.
The final refinement is the use of information related to short
sales concurrent with information from insider trading. Since short
sellers are believed to possess superior information relative to the
market, stocks with significant insider selling are likely to
underperform the market if they also have an abnormally high level
of short interest. Similarly, stocks with a buy recommendation based
on insider trading are likely to outperform the market if they also
have a low level of short interest. Thus, the level of short interest
can be used to verify the information provided by insider trading.
The evidence presented in this chapter and the trading strategy rec-
ommendations are based on past data. Since future market condi-
tions and market patterns may be completely different, insider
trading may not continue to predict future price movements. More-
over, the refinements and other uses suggested in “Other Uses and
Refinements of Insider Trading Information” are untested even with
Beyond the Random Walk158
prior-period data. Finally, the trading strategies based on insider
trading may be considerably riskier than holding funds in the
• Contrary to popular belief, most trades by insiders are legal.
Insiders may trade to raise funds, or they may believe that their
company’s stock is misvalued by the market. Whenever insid-
ers trade for reasons other than liquidity, they convey infor-
mation about their personal beliefs to the market. As insiders
know and understand the company better than the market, it
is reasonable to expect that mimicking insiders’ trades is a prof-
• The evidence suggests that top executives know more. Large
trades (up to 500,000 shares) reveal more. Purchases have bet-
ter predictive ability than sales. Consensus among insiders is
important. It is easier to forecast returns for smaller firms than
for larger firms. Copying carefully selected insider trades can
generate large abnormal returns, typically between 10 and 15
percent per year.
• Recent changes in SEC reporting regulations and advances in
sharing information via the Internet make the disclosure of
insider trades much quicker than before. These changes should
help in making insider trading more profitable to outsiders.
• Insider trading information can be used to construct trading
strategies. However, it is difficult and expensive to get insider
trading data. It may be necessary to rely on published infor-
mation in secondary sources. Starting with stocks covered by
the “Insider Trading Spotlight” of the Wall Street Journal and
applying the criteria enunciated in “Evidence,” it is possible to
make definite buy and sell recommendations. The six-month
returns to these buy and sell recommendations are quite large.
Firms with a buy recommendation earn an abnormal return of
28.8 percent over a six-month period, whereas stocks with a
sell recommendation lose 14.8 percent during the same period.
• Insider trading information can be used for other purposes as
well. It can be used to predict the broad market direction. Also,
investors can look up information on insider trades before ex-
ecuting their personal trades. If insiders have been selling, then
Trading by Insiders 159
it is advisable not to buy. But if insiders have been buying their
own stock or not selling their stock, then buying that stock may
be a smart decision.
Copying insider trades is profitable. As insiders generally know a lot
more about their companies than outsiders and the market, trades by
insiders convey new information to vigilant outsiders. This informa-
tion can be used in a variety of ways. First, trading strategies based
on this information can generate annual abnormal returns of 10–15
percent. Second, the information can be used to review an investor’s
own trades. Third, the information can even suggest whether the
overall market or a particular industry is likely to fall or rise.
Information on Trades by Insiders for Individual Stocks
http://www.quicken.com: Type in the ticker symbol. After quote information is
displayed, click on “Insider Trading” in the left menu column. The Quicken
site is very user-friendly, so try this one first. To double-check, go to the
Vickers Stock Research site, which has the primary information on which the
data on the Quicken site are based.
http://www.vickers-stock.com: This site has the most information compared to
any other site. Sometimes there is too much information, and that is why the
Quicken site is recommended as the first stop when you need information
on individual stocks. The site also reports its own “Insider Index” based on
insider sells and buys for each stock. An exploration of the site reveals that
the former chairman of the board of directors of Enron, Ken Lay, sold nearly
half a million shares of Enron, worth more than $25 million, between
January 2001 and July 2001.
http://www.wallstreetcity.com: Enter the ticker symbol, press Enter, and then
click on “Insider Trading” to get details of trades by insiders. In addition to
firm-by-firm insider trades, you can also get information on the best
industries based on insider trading. To do that, click on “Industry Groups”
below “Insider Trading.” Thereafter, select “All Industries” and “Insider
Trading” in the drop-down menus near the top of the site. Then click on
“Insider Rank” to sort by the best industry down to the worst. The source of
the data on this site is Vickers Stock Research.
http://insider.thomsonfn.com: Thomson Financial’s site is for institutional
investors. To get insider trades by company, type in the ticker symbol and
press Enter. The “Market Tearsheet” provides the overall market sentiment.
This site’s measure is based on dollar value, whereas Vickers’ weekly
“Insider Index” is based on the number of insiders who bought or sold. Data
for the Wall Street Journal’s “Insider Trading Spotlight” comes from this
particular site (go to “Ideas” on this site).
Beyond the Random Walk160
http://finance.yahoo.com: Type in the ticker symbol and go to “Profile.” Click
on “Insider Trading Data” (to the right of “Officers,” the title of the section
where the officers of the company are listed). Provides insider trading
information by company. The source of this data is EDGAR Online.
http://www.marketguide.com: Registration is required to access information
on the website. Detailed insider trading information can be obtained by
clicking on “Insider Trading.” Summarized information is available under
http://money.msn.com: Provides insider trading information by company. This
list is updated weekly on Friday and is based on Form 4 SEC filings received
from Disclosure Inc. The filings are delivered to MSN Money one week after
they are received by Disclosure.
http://www.edgar-online.com: This site requires subscription. However, basic
data from this site can be obtained through http://finance.yahoo.com
http://www.thomsoninvest.net: Thomson Financial’s site for individual
investors. The site has two recommendations under “Opinion.” You can
obtain insider trading information by typing in the company’s ticker
symbol. It also gives CDA/Investnet’s rating based on trading by insiders.
However, the site does not provide firm-level data on trading by insiders.
Thomson Financial is the holding company for numerous financial compa-
nies such as First Call, Data Stream, Securities Data Company, Disclosure,
Dialog, CDA/Investnet, Investment Dealers’ Digest, and so on. It is also the
publisher of the discontinued newsletters Insider Chronicle and Insider Scores.
http://www.wsj.com: The Wall Street Journal lists the top ten insider sales and
purchases in the “Insider Trading Spotlight” column every Monday online
and on Wednesdays in print. The source of its data is “Ideas” on http://
http://www.sec.gov: For original filings by insiders.
Newsletters Based on Trading by Insiders
Discontinued newsletters: Insider Chronicle, Insider Scores, Inside Track, and Insider
http://www.argusgroup.com: Site of Vickers Stock Research. Offers a variety of
reports for purchase: Vickers Insider Trading Report and Vickers Weekly Insider.
Vickers Insiders Portfolio has been followed by Hulbert Financial Digest since
December 1992. Outperforms the market on an absolute basis and a risk-
adjusted basis. Vickers Insiders Portfolio earned an annualized return of 11.2
percent from 1993 to June 2002, compared with 10.5 percent for the Wilshire
http://www.jackadamo.com: Jack Adamo’s weekly newsletter, called Insiders
Plus, has been followed by Hulbert Financial Digest since January 2001.
According to HFD, the newsletter has outperformed the market since
January 2001, earning a return of –10.2 percent from February 2001 to June
2002, compared to –17.9 percent for the market. However, this is too short a
period for evaluation. Jack Adamo’s earlier newsletter, Inside Track, probably
did not do well, seeing as he discontinued its publication and replaced it
with Insiders Plus.
http://www.theinsiderreport.com: Weekly newsletter recommends one stock
and provides a “Strong Buy” list based on trading by insiders. No informa-
tion about its performance is available from independent sources.
Trading by Insiders 161
References for Further Reading
Benesh, Gary A., and Robert A. Pari. 1987. Performance of Stocks Recommended
on the Basis of Insider Trading Activity. Financial Review 22(1), 145–58.
Bernhardt, Dan, Burton Hollifield, and Eric Hughson. 1995. Investment and In-
sider Trading. Review of Financial Studies 8(2), 501–43.
Bettis, Carr, Don Vickrey, and Donn W. Vickrey. 1997. Mimickers of Corporate
Insiders Who Make Large-Volume Trades. Financial Analyst Journal 53(5), 57–
Bettis, J. Carr, Jeffrey L. Coles, and Michael L. Lemmon. 2000. Corporate Policies
Restricting Trading by Insiders. Journal of Financial Economics 57(2), 191–220.
Chang, Saeyoung, and David Y. Suk. 1998. Stock Prices and the Secondary Dis-
semination of Information: The Wall Street Journal’s “Insider Trading Spotlight”
Column. Financial Review 33(3), 115–28.
Damodaran, Aswath, and Crocker H. Liu. 1993. Insider Trading as a Signal of
Private Information. Review of Financial Studies 6(1), 79–119.
Eckbo, B. Espen, and David C. Smith. 1998. The Conditional Performance of In-
sider Trades. Journal of Finance 53(2), 467–98.
Ferreira, Eurico J., and LeRoy D. Brooks. 2000. Re-Released Information in the
Wall Street Journal’s “Insider Trading Spotlight” Column. Quarterly Journal of
Business and Economics 39(1), 22–34.
Friederich, Sylvain, Alan Gregory, John Matatko, and Ian Tonks. 2002. Short-Run
Returns Around the Trades of Corporate Insiders on the London Stock Ex-
change. European Financial Management 8(1), 7–30.
Kahle, Kathleen M. 2000. Insider Trading and the Long-Run Performance of New
Security Issues. Journal of Corporate Finance 6, 25–53.
Lakonishok, Josef, and Inmoo Lee. 2001. Are Insider Trades Informative? Review
of Financial Studies 14(1), 79–111.
Lee, Wayne Y., and Michael E. Solt. 1986. Insider Trading: A Poor Guide to Market
Timing. Journal of Portfolio Management 12(4), 65–71.
Moreland, Jonathan. 2000. Profit from Legal Insider Trading: Invest Today on Tomorrow’s
News (Chicago: Dearborn Trade).
Pettit, R. Richardson, and P. C. Venkatesh. 1995. Insider Trading and Long-Run
Return Performance. Financial Management 24(2), 88–103.
Roth, Greg, and Andy Saporoschenko. 1999. The Informational Effects of Large
Insider Stock Purchases. Managerial Finance 25(1), 37–48.
Seyhun, H. Nejat. 1986. Insiders’ Profits, Cost of Trading, and Market Efficiency.
Journal of Financial Economics 16(2), 189–212.
——— . 1992. Why Does Aggregate Insider Trading Predict Future Stock Returns.
Quarterly Journal of Economics 107(4), 1303–32.
——— . 1998. Investment Intelligence from Insider Trading (Cambridge, Mass.: MIT
Trivoli, George William. 1980. How to Profit from Insider Trading Information.
Journal of Portfolio Management 6(4), 51–56.
1. Besides the author’s own analysis, this chapter is based on research in
Lakonishok and Lee (2001), Chang and Suk (1998), Bettis, Vickrey, and Vickrey
Beyond the Random Walk162
(1997), Ferreira and Brooks (2000), Roth and Saporoschenko (1999), and, es-
pecially, extensive work by Seyhun (1986, 1992, 1998). Seyhun’s book on trad-
ing by insiders (1998) is strongly recommended for anyone who wants to
learn much more about insider trading.
2. See the section “Implementation Through Sector Fund Newsletters” for a
discussion on evaluation of newsletters.
Firms in the S&P 500 are occasionally replaced by new firms because
the existing firm is no longer representative of the economy or the firm
ceases to exist (goes bankrupt or is acquired by another firm). In gen-
eral, the changes are announced about a week before they become
Evidence indicates that a firm added to the index typically rises in
value, while a firm dropped from the index falls in value. Not all of this
change takes place on the announcement date; rather, it continues to
occur until the effective date. However, after the effective date, the price
change reverses itself. The added firms give up some value, and the
deleted firms regain nearly all of their lost value. There are several ex-
planations for these price movements.
Investors and arbitrageurs can earn abnormal returns by buying (short-
selling) the added firm (deleted firm) upon announcement and revers-
ing the positions on the effective date. The new positions are held for
about a month and then liquidated.
The Standard and Poor’s 500 (S&P 500) is a portfolio of five hun-
dred stocks that represents leading industries in the U.S. economy.1
The S&P 500 is considered to be a good proxy for the U.S. market
and is commonly used in evaluating performance of money man-
agers. The S&P 500 is considered an investable index, that is, indi-
viduals or institutions can easily invest in the stocks in the S&P 500.
Currently, about $1 trillion out of a total market value of about $12
trillion is indexed directly or indirectly to the S&P 500. Changes to
the index are widely followed.
Changes to the S&P 500 Index
Beyond the Random Walk164
Most but not all S&P 500 companies are large. At the end of 2002,
340 firms in the S&P 500 were in the top 500 firms by market capi-
talization. There are many large companies not in the S&P 500, such
as USA Interactive ($11 billion market capitalization at the end of
2002) and Liberty Media ($23 billion). Similarly, there are many small
firms in the S&P 500, such as McDermott International ($275 mil-
lion) and Tupperware ($900 million). The median market value of
S&P 500 firms is about $8 billion.
Not all S&P 500 companies are well-known firms. The typical in-
vestor is aware of companies usually through consumer products
(Coke, Pepsi, Johnson and Johnson, Wal-Mart, etc.) or from coverage
in the media (Enron [since dropped from the index], Honeywell, Tyco
International). Companies with industrial products are hardly ever
recognized. Some large companies that are not well known include
Schlumberger ($32 billion), Applied Materials ($33 billion), Pitney
Bowes ($10 billion), Fifth Third ($35 billion), Automatic Data Pro-
cessing ($36 billion), Medtronic ($62 billion), and AIG ($207 billion).
The Process of Changing
Changes to the S&P 500 index are always initiated by deletions.
About three-quarters of all deletions from the index are involun-
tary due to major restructurings, caused by a merger, spin-off, or
bankruptcy. A deletion may occur when an S&P 500 firm merges
with another company that is already a member of the S&P 500 (for
example, Exxon’s acquisition of Mobil) or is acquired by a foreign
company (Nestlé’ s acquisition of Ralston Purina). The S&P 500 now
contains no foreign companies; the remaining seven were deleted
in July 2002. A spin-off can result in a deletion from the index if the
firm becomes unrepresentative as a consequence of the spin-off. For
example, FMC was deleted from the S&P 500 when it spun off FMC
Technologies. In most cases, though the spun-off firm is added to
the S&P 500. For example, when 3Com spun off Palm, 3Com was
deleted from the S&P 500 and replaced by Palm. Firms filing for
bankruptcy or those likely to file for bankruptcy, such as Kmart and
Global Crossing, are also replaced.
In addition, firms may be deleted voluntarily by Standard and
Poor’s when they cease to represent the economy, either because
the industry is no longer representative of the economy (railroads,
for instance) or because the firm is no longer representative of the
industry (such as Rite Aid for retail drug stores). Since the number
Changes to the S&P 500 Index 165
of firms in the index is maintained at five hundred, additions to the
index are almost always announced at the same time as deletions.2
Standard and Poor’s uses four criteria to pick a firm, although
the criteria are not always strictly enforced. The firm must have
sufficient liquidity. Firm ownership must not be concentrated in a
single or few entities. The firm must be profitable. The firm must be
a leader in an important U.S. industry. Though no explicit market
capitalization is specified as a criterion, the market capitalization of
firms added in 2002 was at least $4 billion. However, because many
firms meet the objective criteria, Standard and Poor’s can ignore
some of those criteria, making changes to the index subjective and
unpredictable. Market observers, however, keep trying to predict
changes to the index. For example, Lehman Brothers identified nine-
teen candidates for addition and ten candidates for deletion at the
end of February 2002. Six months later, only four of the nineteen
firms had been added, and two of ten firms had been deleted—not
a very good record. On the other hand, the June 2002 issue of Money
reported that Goldman Sachs would get added to the S&P 500 by
year’s end. Indeed, it was added to the index in July 2002. As much
fun as it is to try to predict changes to the index, the focus here is on
trading after the changes have been announced.
Changes to the index are announced after the market closes, and
they take place at the close of the effective date. The amount of time
between the announcement date and the effective date varies from
one day to about one month, with an occasional lag of as much as
three months. In most cases, the effective date is announced at the
time of the initial announcement. In the remaining cases, especially
when the merger consummation date is uncertain, the effective date
is announced a few days after the initial announcement.
A change to the S&P 500 index is a significant event for the firm that
is added or deleted. An addition to the index means that there will
be an additional demand for about 8 percent of the outstanding
Second, publicity surrounding the addition will cause many
investors to learn about the firm, and this may influence them to
trade. Third, more analysts are likely to follow the newly added
firm due to a greater interest in the firm. Finally, there will be more
trading in the firm, which can make it more liquid.
The effect of additions on the stock price is presented in Table 8.1,
and the effect of deletions is in Table 8.2. The first period is up to
Table 8.1 Price Impact of Additions to the S&P 500 Index
Abnormal Abnormal Return to Return tol
Additions Return Return 20 Days 60 Days
Total in the on AD+1 (AD+1 to ED) After ED After ED
Period Additions Sample (%) (%) (%) (%)
July 1962–Aug. 1976 304 285 0.0 –0.5 0.9
Sept. 1976–Sept. 1989 297 274 3.0* 2.9* 3.5*
1990 13 11 3.1+
6.7* 3.1 –3.8
1991 13 9 5.8* 8.2* 4.5+
1992 7 6 4.6+
1993 13 9 4.7* 7.3* 5.6+
1994 18 16 2.2* 4.7* 1.2 0.3
1995 32 21 4.3* 7.2* 3.0 2.5
1996 27 20 3.8* 7.5* 2.9 3.8
1997 28 24 8.1* 10.5* 7.5* 5.8
1998 48 37 5.5* 9.3* 3.5 0.5
1999 41 38 5.8* 8.5* 6.0 7.8
2000 33 29 7.1* 10.7* 13.5* 12.5+
1989–2000 278 224 5.3* 8.4* 5.6* 4.5*
All announcements are made after market close on the announcement date indicated in the table. AD+1 refers to the first trading day after announcement. ED
refers to the effective date. All changes become effective at the close on the effective date. Volume is the sixty-day average prior to announcement date. Size is the
market capitalization as of the day before announcement. Abnormal return is calculated as raw return minus the S&P 500 return. Statistical significance is at better
than 1 percent for returns marked with * and at better than 5 percent for returns marked with +
Table 8.2 Price Impact of Deletions from the S&P 500 Index
Abnormal Abnormal Return to Return to
Deletions Return Return 20 Days 60 Days
Total Considered on AD+1 (AD+1 to ED) After ED After ED
Period Deletions Here (%) (%) (%) (%)
July 1962–Aug. 1976 304 170 –0.3 1.6* 3.5*
Sept. 1976–Sept. 1989 297 61 –1.6 –3.8+
1990 13 5 –1.6 –4.6 –9.1 43.7+
1991 13 4 –19.3 –19.3 20.1 21.4
1992 7 5 –10.2 –32.4* 6.0 8.2
1993 13 6 –2.3 –7.2 –4.9 3.3
1994 18 10 –2.8+
1995 32 11 –5.8+
–15.7* –10.7* –16.7
1996 27 13 –4.0* –7.4* –0.1 3.0
1997 28 4 –5.2+
1998 48 8 –7.3* –10.5+
1999 42 9 –3.2 –3.3 2.8 4.4
2000 32 12 –5.9* –10.9* –11.9+
1989–2000 278 88 –5.4* –10.3* –3.3 2.6
Returns are reported in decimals. All announcements are made after market close on the announcement date indicated in the table. AD+1 refers to the first trading
day after announcement. ED refers to the effective date. All changes become effective at the close on the effective date. Volume is the sixty-day average prior to
announcement date. Size is the market capitalization as of the day before announcement. Abnormal return is calculated as raw return minus the S&P 500 return.
Statistical significance is at better than 1 percent for returns marked with * and at better than 5 percent for returns marked with +
Beyond the Random Walk168
August 1976, when indexing was not considered important or popu-
lar. Until that time, no public announcements were made. The sec-
ond period starts in September 1976, when Standard and Poor’s
began to formally announce the changes to interested investors, the
media, and especially mutual fund managers. During this period,
changes were announced after market close on Wednesdays, and
the change in the index became effective the next morning upon
opening. Since index fund managers are concerned with minimiz-
ing tracking error (the difference between the fund return and the
S&P 500 return), index funds must buy the stock at the time of its
addition to the index. However, with the growth in indexing, the
buy orders from index funds at the market open increased order
imbalances and volatility. To ease order imbalances, Standard and
Poor’s began preannouncing the changes on October 1, 1989. Thus,
the third period covers changes to the S&P 500 from October 1989
to the present. Returns for both additions and deletions are reported
after adjusting for the market return as measured by the total re-
turn to the S&P 500 index.
It is interesting to contrast the three periods. During the 1962–76
period (Table 8.1), when no public announcements were made, noth-
ing abnormal happens to the stock price either on the first trading
day after announcement or anytime after that. It is basically a non-
event. During the 1976–89 period, when the stocks were added im-
mediately after announcement, all the action is on the announcement
date and nothing thereafter. The price goes up abnormally by 3 per-
cent immediately after announcement but tracks the S&P 500 index’s
return for the next twenty trading days (about one calendar month)
and for the next sixty trading days (about three calendar months).
There is a lot of action in the 1989–2000 period. Overall, the return
following the announcement date is an abnormal 5.3 percent, which
climbs to 8.4 percent by the effective date and then falls back to the
announcement date return twenty trading days later. It seems that
there is a pop around the effective date that disappears later on.
Since the number of firms is kept constant at five hundred, there
must be one deletion for every addition. However, the sample of
deletions considered in Table 8.2 is much smaller. Deletions that
occurred due to a bankruptcy, merger, or other major corporate
events are excluded from the table. Only deletions that are made
Changes to the S&P 500 Index 169
voluntarily by Standard and Poor’s and where the firm continues
to exist are included.
no public announcements were made, nothing abnormal happens
around the announcement. During the 1976–89 period, again no sig-
nificant abnormal change in price occurs around the announcement,
and the magnitude of the change is also small. The abnormal return
after announcement for the first and second periods are of opposite
signs: the price rises abnormally in the first period but falls abnor-
mally in the second period. Overall, for the first two periods, it is
reasonable to conclude that the deletions have no impact on price.
As with additions, there is much action in the period after 1989.
Deleted firms fall 5.4 percent on the day of announcement, fall an-
other 4.9 percent by the effective date for a total loss of 10.3 percent,
rebound back to a net loss of 3.3 percent twenty days later, and fi-
nally post a gain of 2.6 percent sixty days after the effective date. It
can be seen that the net effect on stock price of deletions is zero.
Although the year-by-year results from 1990 to 2000 vary widely,
there is a common theme. The announcement date return is nega-
tive, and the return by the effective date becomes even more nega-
tive. Thereafter, in most years, the total return is less negative twenty
days later and much less negative or even positive sixty days later.
There are five explanations for the price impact of index changes:
imperfect substitutes, price pressure (temporary), certification, li-
quidity, and investor recognition. However, none of the explana-
tions seems capable of fully explaining the price effects.
The common starting point for these explanations is market effi-
ciency. If markets are informationally efficient, then the price of a
stock should not change unless there is new information. This means
that excess demand or excess supply unaccompanied by new infor-
mation should not affect security prices. How can that happen? The
idea is that financial assets are perfect substitutes for one another,
and the market is huge.Any single supply or demand shock is small
compared to the overall size of the market. And since financial as-
sets are perfect substitutes, excess demand for a stock will be met
by arbitrageurs. They will short-sell that stock, increasing its sup-
ply, and will buy another stock with equivalent risk-return charac-
teristics. In such an event, any price change will be imperceptible.
However, as reported in the previous section, there is a permanent
Beyond the Random Walk170
price impact. If there is no new information associated with index
changes, then the only reason for the price impact is that financial
assets do not have perfect substitutes.
The assumption of no new information, however, is questionable.
For example, the observed change in stock prices could occur due to
a change in expected future cash flows for at least two reasons. First,
inclusion in the S&P 500 might convey positive information about
the longevity and prospects of that firm, resulting in an upward revi-
sion of expected future cash flows. This is called certification.
The price impact could also be consistent with perfect substitut-
ability if a decrease in required return accompanies an index addi-
tion. This could happen for several reasons. First, there may be an
improvement in liquidity because of higher trading volume or lower
asymmetry of information among traders. Second, the improvement
in liquidity may occur because of greater production of informa-
tion, resulting in the reduction of variability of earnings and other
relevant estimates. Improvement in liquidity means that the cost of
transacting will fall, causing the price to increase.
The third reason proceeds from investor recognition. An increase
in investor awareness, for example, can affect the stock price in sev-
eral ways. First, the firm’s operating performance may improve
because of increased monitoring by investors and by enhanced ac-
cess to capital markets. Second, the firm’s liquidity may improve
due to less information asymmetry as a result of greater production
of information by investors and analysts.
The imperfect-substitutes argument relies on the concurrent growth
in indexing and the price impact of changes to the S&P 500. There is
a permanent price increase for firms added to the S&P 500 index
(see Table 8.1). There are two arguments to suggest that there is no
new information. First, before the advent of indexing (between 1962
and 1976), there was no price change. If an index addition is accom-
panied by information, then the price change should have occurred
during that period. Second, in selecting firms Standard and Poor’s
relies only on publicly available information, which implies that no
new information is implicit in an index change. Price changes could
also occur if there is a permanent improvement in liquidity. How-
ever, in general, there is little evidence of an improvement in liquid-
ity. Thus, the only remaining explanation is that the price increase
must be due to the demand shock created by indexers. Since stocks
have imperfect substitutes, the stock added to the index increases
Changes to the S&P 500 Index 171
in price. If stocks did have perfect substitutes, the arbitrageurs would
have ensured a negligible price effect.
There are two pieces of evidence that do not support the imper-
fect-substitutes explanation. First, in the post-1976 period, there is
no relation between the level of indexing and the price impact. If
the imperfect-substitutes argument is worthy of support, then the
greater the demand shock, the greater should be the price impact.
That does not happen. Second, the imperfect-substitutes explanation
should work for both additions and deletions. Table 8.2 shows that
firms deleted from the index do not have a permanent price impact.
This is also inconsistent with the imperfect-substitutes explanation.
Thus, it would seem that the imperfect-substitutes explanation is not
The price pressure argument also relies on imperfect substitutes
except that the focus is on short-term price changes. Under this ex-
planation, adding a new stock to the index generates extra demand
for the stock. This extra demand generates an upward price pres-
sure to persuade investors to sell the stock prematurely. The price
pressure abates once the momentary demand is satisfied.
Tables 8.1 and 8.2 show that until 1989 there is virtually no price
pressure and the initial price impact is never reversed. The price
pressure becomes more of an issue in the period after 1989, when
the preannouncement procedure becomes effective. As discussed
in the previous section, activities of the arbitrageurs seem to con-
tribute to the price pressure. Thus, the price pressure does not oc-
cur due to demand shocks but is artificially created by market
participants in anticipation of price pressure.
There is conflicting evidence on improvement in liquidity, irrespec-
tive of its cause. If adding a stock to the Standard and Poor’s index
increases trading, then the increase in liquidity would cause lower
bid-ask spreads. The lower cost of trading must be reflected in a
price increase around the announcement. On the other hand, the
number of shares available for trading will fall because index funds
generally buy and then hold the shares. The reduction in the shares
available for trading may negatively impact liquidity. There are a
few studies that find a permanent increase in liquidity, as deter-
mined by permanent increases in trading volume, and permanent
Beyond the Random Walk172
decreases in quoted and effective spreads. Other studies, however,
find only a temporary improvement that disappears quickly after
the effective date.
The certification explanation maintains that the addition of a stock
to the S&P 500 index conveys new positive information about the
stock. Though Standard and Poor’s relies on publicly available in-
formation, S&P’s analysis of that information suggests longevity
and/or leadership in the firm’s industry. One test of certification is
whether additions or deletions to supplementary indexes, where
the level of indexing is small or nonexistent, affect prices. Indeed,
they do. Additions to supplementary indexes also experience a sig-
nificant abnormal return.
However, what is not easily explained is why there were no price
reactions to additions to the index prior to 1976. Moreover, in the
case of deletions, there is no permanent price impact even in the
most recent years. These observations are inconsistent with a role
of certification in index changes.
Investor awareness of a firm through addition to the S&P 500 index
can help the firm with monitoring and improved access to capital
markets. Monitoring by investors may induce the firm to become
more efficient, thereby improving operating performance. Greater
access to capital markets following membership in the S&P 500 in-
dex may enable it to accept projects that it could not otherwise pur-
sue. Financial institutions may be more willing to lend to indexed
firms, leading to higher debt capacity and/or lower cost of debt.
The additional capital will allow the company to grow at a rate
higher than that prior to inclusion in the index.
For deletions, however, investors cannot become “unaware” of
the stock, though they may attempt to reduce their holdings. The
investor recognition explanation suggests an asymmetric effect:
positive price impact for additions and a muted price impact for
deletions. The results in Tables 8.1 and 8.2 are consistent with this
How does this explanation square with other evidence? Since no
public announcements of index changes were made before 1976,
investors could not become aware of the stock, and hence there was
no price impact. Besides index changes, a similar argument works
for neglected stocks. Whenever neglected stocks are prominently
Changes to the S&P 500 Index 173
featured in the media, they tend to become more widely held, re-
sulting in a price increase. This implies that investor awareness is
an important consideration for pricing of securities.
There are at least five explanations for the price impact of index
changes. Of these, the investor recognition explanation is the one most
consistent with the evidence. However, it is popularly believed that
the imperfect-substitutes explanation is the more appropriate one.
Reliance on an incorrect explanation can make market participants
misjudge price patterns, especially with regard to deletions.
Index effect can be divided into two parts: permanent and tempo-
rary. The permanent index effect is not a mispricing and cannot be
arbitraged. In the case of additions, there are both permanent and
temporary effects. The permanent index effect is the abnormal re-
turn on the day following the announcement. The abnormal return
between the announcement date and the effective date is a tempo-
rary effect that eventually disappears. The evidence in Table 8.1 also
shows the transitory nature of the price increase for additions. Stan-
dard and Poor’s own evidence corroborates the conclusions enu-
merated here. It states that “a stock being added to the index would
rise about 8.5 percent between announcement and implementation
dates. . . . The stock would also give back half or more of that gain
over the next year.”
In the case of deletions, however, there is no permanent index
effect. All of the abnormal return is temporary, as can be seen from
Table 8.2. Again, Standard and Poor’s essentially reaches the same
conclusion: “The average market decline across all the deletions since
1998, a total of 53, was 11.7 percent. On average, this decline was
nearly fully reversed by the sixth trading day.”
Why does the temporary index effect occur, and why does it per-
sist? The primary reason for persistence is the focus on tracking
error by index fund managers. Index fund managers are evaluated
strictly on the size and volatility of the tracking error (difference
between the fund’s return and the S&P 500 return) and not on the
direction of the tracking error.Amanager of a large index fund (more
than $1 billion) is not expected to have a tracking error of more than
0.03 percent in a year. If it is more than 0.10 percent, the manager is
Beyond the Random Walk174
likely to be fired. Therefore, it is easy to see that the managers are
constrained, and must buy (sell) the firm added to (deleted from)
the index on the effective date at the close.
Arbitrageurs know this. So they buy the stock added to the index
before the effective date knowing that they will be able to unload
the stock to the index fund managers at a higher price. The demand
from the index fund managers is sufficient to absorb the entire sup-
ply of the arbitrageurs.
The situation is even more exciting in the case of deletions. Be-
lieving the imperfect-substitutes explanation, arbitrageurs force
down the price of stocks deleted from the index on the first trading
day after announcement by short selling. The price continues to fall
until the effective date, when the arbitrageurs repurchase the de-
leted stocks from index fund managers. The price of the deleted
stocks recovers soon thereafter.
There are two factors that cause the temporary index effect. If
either of them changes, the temporary index effect will disappear.
First, the preannouncements by Standard and Poor’s allow the
arbitrageurs to play this game. If the change in the index takes place
immediately, the arbitrageurs will not be able to time their trades to
the detriment of index fund managers. The second reason is the
way owners of index funds evaluate the index fund managers. The
performance of an index fund manager is measured by the tracking
error, which forces the managers to trade exactly at the time that
changes to the index are implemented. If the managers were free to
trade the stocks deleted from or added to the index within a reason-
able period around the effective date, they will not be forced to play
into the hands of the arbitrageurs, and the investors will actually
gain from this limited freedom given to the managers.
Trading Around the Effective Date
This section expands on the evidence presented above suggesting
that a temporary price effect around the effective date is available
for trading. Data for the year 2001 are selected for analysis for two
reasons. First, they bring the evidence in prior sections more up to
date. Second, observers have commented that 2001 was not a prof-
itable year for arbitrageurs engaged in taking advantage of known
price patterns around index changes. For example, Lehman Broth-
ers’ comment in the March 4, 2002, issue of Outlook is illustrative:
“[W]e find that not only have stocks underperformed the index
during their index inclusion period [announcement to effective date]
Changes to the S&P 500 Index 175
but they also underperformed the index post-inclusion date.” There
are two possible explanations for the weak index effect: either the
negative market trend throughout the year attracted significantly
more arbitrage funds or the shorter period between the announce-
ment and effective date limited the ability of arbitrageurs to time
RETURN PATTERNS BEFORE AND AFTER EFFECTIVE DATE
Tables 8.3 and 8.4 contain the list of additions and deletions during
2001. Index changes along with the announcement date and the ef-
fective date are obtained from Standard and Poor’s website. Stan-
dard and Poor’s makes the announcement around 5:15 P.M. on the
announcement date, and the change becomes effective at the close of
trading on the effective date. A list of effective dates is available un-
der “Index Changes,” and announcements related to those changes
are available under “News” on the S&Pwebsite (www.spglobal.com).
The announcement states the reason for the change if the change is
involuntary. Involuntary changes to the index are excluded from fur-
ther consideration and the reasons for exclusion are recorded in Tables
8.3 and 8.4. In addition, if a major corporate event occurs in the week
prior to the change announcement or if an earnings release is sched-
uled to occur anytime between the announcement date and the effec-
tive date, then that firm is also excluded from consideration.
Figure 8.1 The cumulative return from the day of announcement of change to the
effective date and until twenty days after the effective date is shown for additions
and deletions from the S&P 500 index during 2001.
Changes to the S&P 500 Index
0 Ann. Day Effective
ED + 5 ED + 20
Table 8.3 Additions to the S&P 500 Index During 2001
Prior to Volume
Reason for Announce- as a % of
Ticker Exclusion, ment Shares
Name Symbol if Any (in $millions) Outstanding
1 Waters WAT 5,000 0.46
2 Jones Apparel JNY 4250 0.94
3 Genzyme GENZ 12,200 1.02
4 Equity Residential EQR 7,500 0.24
5 Nvidia NVDA 7,425 3.24
6 Health Management HMA 4,800 0.50
7 TECO Energy TE 3,825 0.27
8 Equity Office EOP 13,100 0.30
9 Immunex IMNX 9,600 0.58
10 XL Capital XL 9,750 0.40
11 International Game IGT 3,900 1.41
12 CIENA CIEN 5,700 2.77
13 Amerisource ABC merged firm
14 Zimmer Holdings ZMH spin-off
15 Family Dollar Stores FDO 4,950 0.47
16 PMC Sierra PMCS 5,000 2.37
17 AT&T Wireless AWE spin-off
18 Rockwell Collins COL spin-off
19 John Hancock JHF 12,000 0.26
20 Zions Bancorp ZION 5,200 0.25
21 TMP Worldwide TMPW 5,900 1.08
22 Pepsi Bottling PBG 6,000 0.34
23 Mirant MIR spin-off
24 Concord EFS CEFT earnings news
25 Fiserv FISV 5,880 0.40
26 Cintas CTAS earnings news
27 Citizens CZN 3,550 0.15
28 Univision UVN 5,400 0.85
29 Jabil Circuit JBL 4,375 2.60
30 Noble Drilling NE 5,500 1.45
All announcements are made after market close on the announcement date indicated in the
table. All changes become effective at the close on the effective date. Volume is the sixty-day
average prior to announcement date. Size is the market capitalization as of the day before
announcement. Abnormal return is calculated as raw return minus the S&P 500 return. Vol-
ume turnover is reported as volume divided by the number of shares outstanding. Since Nasdaq’s
reported volume is approximately two times the true volume, Nasdaq’s volume is divided by
Table 8.4 Deletions from the S&P 500 Index During 2001
Prior to Volume
Reason for Announce- as a % of
Ticker Exclusion, ment Shares
Name Symbol if Any (in $millions) Outstanding
1 FMC FMC spin-off
2 Homestake Mining HM merger
3 Ralston Purina RAL merger
4 National Service NSI spin-off
5 Enron ENE bankruptcy
6 GPU GPU merger
7 Global Crossing GX news
8 Texaco TX merger
9 Tosco TOS merger
10 Wachovia WB merger
11 Broadvision BVSN low price
12 American General AGC merger
13 Oneok OKE 1000 0.32
14 Timken TKR 1000 0.18
15 Cabletron Systems CS spin-off
16 Quaker Oats OAT merger
17 Potlatch PCH 1000 0.45
18 Long Drug Stores LDG 900 0.46
19 Harcourt General H merger
20 Alza AZA merger
21 CIT Group CIT merger
22 Adaptec ADPT spin-off
23 Briggs& Stratton BGG 900 7.4
24 Ceridian CEN spin-off
25 Old Kent Financial OK merger
26 Summit Bancorp SUB merger
27 U.S. Bancorp USB merger
28 Union Carbide UK merger
29 Coastal CGP merger
30 Time Warner TWX merger
All announcements are made after market close on the announcement date indicated in the
table. All changes become effective at the close on the effective date. Volume is the sixty-day
average prior to announcement date. Size is the market capitalization as of the day before
announcement. Abnormal return is calculated as raw return minus the S&P 500 return. Vol-
ume turnover is reported as volume divided by the number of shares outstanding. Since Nasdaq’s
reported volume is approximately two times the true volume, Nasdaq’s volume is divided by
Abnormal Abnormal Abnormal
Number of Return Return Return
trading days Abnormal from from from
Announce- between Return on AD+2 ED+1 ED+1 to
ment Effective AD AD+1 to ED to ED+5 ED+20
Date (AD) Date (ED) and ED (%) (%) (%) (%)
8/27/2001 8/29/2001 2 –3.3 3.6 1.3 9.5
7/31/2001 8/6/2001 4 –7.5 –4.1 5.3 13.3
6/27/2001 7/6/2001 6 –5.1 –5.4 3.8 7.9
6/25/2001 6/29/2001 4 –5.3 –4.7 1.9 5.2
3/27/2001 4/2/2001 4 –2.7 –4.9 7.7 1.9
–4.8 –3.1 4.0 7.6
Beyond the Random Walk180
After screening based on the above criteria, twenty-three additions
and five deletions remain out of the total sample of thirty additions
and thirty deletions in 2001. Consider the additions in Table 8.3. Nearly
all of the additions are firms with at least $4 billion in market capitali-
zation. More importantly, in all but four cases, the waiting time is one
week or less. Four cases had longer waiting times because of the un-
certain completion of mergers. It seems that Standard and Poor’s has
deliberately reduced the waiting period for the change to become
effective, possibly to curb arbitrage activity.
From Table 8.3, it can be seen that the average return on the first
trading day after announcement of an addition is 4.3 percent. In
addition, added firms earn an additional 2.0 percent thereafter
through the effective date. After the effective date, the added firms
lose 1.4 percent in the next five business days and lose a total of 2.4
percent in the twenty business days after the effective date.
It is instructive to compare and contrast the evidence for 2001
with the evidence given earlier. Prior evidence implies two trading
strategies for additions. Both strategies are based on the price in-
crease around the effective date. The first strategy calls for buying
the added firm immediately upon announcement and selling it on
the effective date. The second strategy requires short-selling the
added firm on the effective date and repurchasing it several days
later. Implementation of both strategies in 2001 is much weaker.
Five deletions remain, as shown in Table 8.4. The price pattern
for deletions is much cleaner and stronger than for additions. The
announcement return is –4.8 percent, which is followed by an addi-
tional –3.1 percent until the effective date. The loss in value is al-
most completely recouped in the twenty business days following
the effective date. Thus, the strategies relating to deletions were as
profitable in 2001 as in earlier years. Perhaps arbitrageurs don’t fully
understand price movements around deletions and are therefore
unable to exploit them.
TEMPORARY PRICE EFFECT UNTIL THE EFFECTIVE DATE
Tables 8.1 and 8.2 reveal that the price of stocks added to the index
increases until the effective date and the price of stocks deleted from
the index decreases until the effective date. Why does this happen?
The consensus is that arbitrageurs have started playing the “S&P
game” with the preannouncements, as explained in the section titled
“Persistence.” With additions, arbitrageurs or market participants
know that the index fund managers must buy the stock at the close
of the effective date. Therefore, the arbitrageurs buy the stock be-
Changes to the S&P 500 Index 181
fore the effective date in the hope of unloading it to the index fund
managers at a higher price on the effective date. For deletions, it is
exactly the opposite.
A question that arises is why index fund managers don’t buy
immediately upon announcement instead of waiting till the effec-
tive date. The index fund managers must wait because their objec-
tive is not to beat the index but to minimize tracking error. To
minimize tracking error, they must buy the added stock at the time
and at the price that Standard and Poor’s adds it to the index, nei-
ther before nor after. Since Standard and Poor’s makes the change
at the close on the effective date, index fund managers have no choice
but to wait.
The most important determinant of the temporary price effect—
that is, the change in price from announcement to the effective date—
is the number of days in that period. If the change becomes effective
the next trading day, then trading becomes almost impossible and
arbitrageurs do not attempt to artificially affect the price. As the
period lengthens, the potential for arbitrage activity increases. A
span of at least three days between announcement and effective date
is required for implementing any trading strategy.
The Trading Process
All trading strategies listed here are based on trading individual
stocks. Exchange-traded funds, mutual funds, and futures cannot
be employed because they contain a basket of stocks, whereas the
strategy calls for a specific stock. Stock options are a possibility for
trading on the temporary index effect and should be explored as an
alternative. However, since the trading costs of options are usually
high, they are not considered here.
The starting point for additions is the announcement of index
changes by Standard and Poor’s, usually between 5:00 P.M. and 6:00
P.M. Major news services will carry the press release. It is also pos-
sible to get the news from Standard and Poor’s website. Once an
addition is identified, follow these steps. There are two trading strat-
egies that can be executed. One is from the announcement date to
the effective date, and the other is from the effective date until about
twenty trading days later.
Beyond the Random Walk182
Primary Strategy for Additions
Step 1: Almost all additions to the index are candidates for trading.
Stocks added to the index are usually actively traded and have low
bid-ask spreads, making the trading costs relatively low. The pri-
mary source of gains for additions is price patterns around the effec-
tive date (see “Trading Around the Effective Date”). If the effective
date for the addition is one or two business days after the announce-
ment, then those additions must be excluded because such additions
are unlikely to garner a significantly large temporary price effect.
Step 2: Avoid stocks with scheduled announcements, such as earn-
ings announcements, up to the effective date. These announcements
will add unnecessary volatility. Moreover, the added firm should not
be a new firm created from an existing firm, like a spin-off or a merger.
The firm should be an existing firm not currently in the index.
Step 3: Place a market order to buy around the close of the first
trading day following the announcement. The reason for waiting
until the end of the day is to ensure that all the excess demand has
been satisfied and the stock has settled to a stable price. The evi-
dence presented for this strategy is based on the closing price. (To
hedge against severe market movements and to reduce the risk of
the trading strategy, consider short-selling the S&P 500 index
[AMEX: SPY]. Also, see Appendix C.)
Step 4: Hold the stock till the effective date. Place a limit order at
the market price to sell all shares held around 10:00 A.M. on the ef-
fective date. Remember the price tends to fall on the effective date.
This concludes the first trading strategy. (If you hedged against
market movements in the previous step, then undo the hedge by
repurchasing the S&P 500 index.)
Secondary Strategy for Additions
Step 1: The second trading strategy requires short selling. Not all
stocks may be candidates for this strategy. Two requirements must
be satisfied. First, the stock must have a relatively narrow spread,
not more than 0.5 percent in any case. Second, the temporary price
effect must exceed 2–3 percent. Otherwise, it is not advisable to try
to capture the post-effective date reversal.
Step 2: Assuming the reversal after the effective date is attractive,
the ideal time to short-sell is in the morning on the day after the
effective date. However, short selling at the close on the effective
date will not be much worse, and the trading results are presented
on this basis. After the short sell order is filled, place an open order
to repurchase the stock at a price that reflects a drop in price equal
Changes to the S&P 500 Index 183
to about one and a half times the expected reversal after the effec-
tive date. (Once again, to hedge against severe market movements
and to reduce the risk of the trading strategy, consider purchasing
the S&P 500 index.)
Step 3: If the open order does not get executed, then close the
position twenty trading days later. (If you hedged against market
movements in the previous step, then undo the hedge by selling the
S&P 500 index.)
The trading strategy for deletions from the index is similar to that
of additions. However, there are some important differences, be-
cause the permanent price effect in the case of deletions is zero,
unlike additions, where the permanent effect is positive. Moreover,
for most investors who do not want to short-sell, the period be-
tween the announcement date and the effective date is attractive for
additions, whereas the time after the effective date is most reward-
ing for deletions.
Deletions are identified from Standard and Poor’s and the news
media. Once a deletion is identified, follow these steps to ensure
that the short-listed deletions consist of only those firms that have
been voluntarily deleted from the index by Standard and Poor’s
and that do not have high trading costs. Two trading strategies ex-
ist for deletions. The primary source of gains for deletions is the
reversal after the effective date. The main trading strategy is de-
signed to capture that reversal.Asecondary trading strategy requires
short-selling the deleted stock on the announcement date to cap-
ture the downward price movement until the effective date.
The secondary strategy is described first because the period for
this strategy (announcement date to effective date) occurs before
the period for the primary strategy. If you are not interested in ex-
ecuting the secondary strategy, skip steps 5, 6, and 7 of that strat-
egy. You still need to follow steps 1 through 4, which describe the
selection of deletions for both strategies.
Secondary Strategy for Deletions
Step 1: Exclude any deletion that is related to a restructuring such
as a merger, spin-off, or bankruptcy. Impending or likely bankrupt-
cies should also be deleted. Look for and exclude deletions that have
had any news related to a major structural change over the prior one
month. This screen usually eliminates 75 percent of the deletions.
Beyond the Random Walk184
Step 2: Stocks with scheduled announcements within two weeks
after the effective date should be avoided. Scheduled announcements
by the firm, such as earnings announcements, add unnecessary
Step 3: The average daily trading volume should exceed one hun-
dred thousand shares a day, so that it is easy to trade without affect-
ing the price. The bid-ask spread should be less than 0.5 percent.
Again, the intent is not to lose a significant portion of the profits to
Step 4: Exclude any stocks that are below the $5 level. Some low-
price stocks might perform as expected, but one must be particu-
Step 5: The secondary strategy is based on short-selling the de-
leted firm after the announcement in anticipation of a further fall in
price. Place an order to short-sell at close on the day following the
announcement date. (To hedge against severe market movements
and to reduce the risk of the trading strategy, consider purchasing
the S&P 500 index.)
Step 6: If the order gets filled, then place an order to repurchase
the stock around 10 percent below the price at which the order is
Step 7: If the open buy order does not get executed, then buy to
close the position as late as possible on the effective date. (If you
hedged against market movements in step 5, then undo the hedge
by selling the S&P 500 index.)
Primary Strategy for Deletions
Step 1: The primary trading strategy attempts to capture the rise
in price of the deleted firm after the effective date. All deletions
selected for the secondary strategy are not automatically candidates
for this strategy. Since the average permanent price effect is zero for
the deletions, the rise in the deleted firm’s stock price, on average,
will be equal to the fall in its price with the effective date. In order to
cover transaction costs and still have a reasonable profit, the abnor-
mal return until the effective date should be more negative than –2
Step 2: For the selected stocks, place an order to buy as close as
possible to the close of trading on the effective date. The morning of
the day following the effective date is preferred. Simultaneously,
place a limit order to sell that reflects an appreciation equivalent to
one and a half times the temporary price effect. Continue to adjust
the limit price by changes in the S&P 500 index return. (Once again,
Changes to the S&P 500 Index 185
to hedge against severe market movements and to reduce the risk
of the trading strategy, consider short-selling the S&P 500 index.)
Step 3: If the open sell order does not get executed, then close the
position twenty trading days later. (If you hedged against market
movements in the previous step, then undo the hedge by repur-
chasing the S&P 500 index.)
In this section, the index effect is implemented for the January-July
2002 period. The month of July 2002 is included because it provides
nine new firms that were added by Standard and Poor’s, including
the replacement of all foreign firms from the index. The results are
in Tables 8.5 and 8.6.
ADDITIONS: BUY ON ANNOUNCEMENT DATE AND
HOLD UNTIL EFFECTIVE DATE
Based on the criteria established earlier, the following firms are
bought at the close of trading on the day after the announcement:
UPS, GS, PRU, EBAY, PFG, ERTS, SPG, MI, and RATL.
The remaining additions are excluded because the difference be-
tween the announcement and the effective date is not more than
two trading days. All nine stocks bought upon announcement are
sold at the 10 A.M. price on the effective date. For ease of computa-
tion, however, all sales are assumed to take place at the close on the
The mean number of days for which a position is held is 6.7 days,
and the mean abnormal return during this period is 6.1 percent.
Assuming a round-trip trading cost of 0.5 percent, the net return is
5.6 percent, which is equivalent to an annualized abnormal return
of over 200 percent.
ADDITIONS: SHORT-SELL ON EFFECTIVE DATE AND
HOLD FOR UP TO TWENTY DAYS
Of the firms selected in the previous subsection, ERTS, SPG, and
RATL are dropped because the temporary price effect is less than
+2 percent. The remaining stocks will be short-sold at the close on
the effective date: UPS, GS, PRU, EBAY, PFG, and MI.
Assuming all of them are successfully short-sold, an open order to
repurchase these shares is placed at a price equal to one and a half
times the temporary price effect. Since the temporary price effect is
Table 8.5 Additions to the S&P 500 Index During January-July 2002
Reason for Prior to Announce-
Ticker Exclusion, Announce- ment
Name Symbol if Any ment Date (AD)
1. Anthem ATH 8300 7/23/2002
2. United Parcel Service UPS* 68150 7/9/2002
3. Goldman Sachs GS* 35400 7/9/2002
4. Prudential Financial PRU* 18000 7/9/2002
5. eBay EBAY* 15850 7/9/2002
6. Principal Financial PFG* 10000 7/9/2002
7. Electronic Arts ERTS* 9200 7/9/2002
8. SunGard Data SDS earnings 6500 7/9/2002
9. North Fork Bancorp NFB 6250 7/12/2002
10. Simon Property SPG* 6,150 6/20/2002
11. Apollo Group APOL 6,350 5/13/2002
12. BJ Services BJS 6,000 5/13/2002
13. American Standard ASD 5,500 5/9/2002
14. First Tennessee FTN 4,850 5/2/2002
15. Marshall & Ilsley MI* 6,200 2/5/2002
16. Rational Software RATL* 4,500 1/23/2002
17. ACE ACE earnings 9,150 1/23/2002
18. MeadWestvaco MWV merged firm 1/23/2002
19. Plum Creek Timber PCL 5,300 1/15/2002
All announcements are made after market close on the announcement date indicated in the
table. All changes become effective at the close on the effective date. Size is the market capi-
talization as of the day before announcement. Abnormal return is calculated as raw return
minus the S&P 500 return.
Table 8.6 Deletions from the S&P 500 Index During January–July 2002
Reason for Prior to Announce-
Ticker Exclusion, Announce- ment
Name Symbol if Any ment Date (AD)
1. Conseco CNC 509 7/23/2002
2. Royal Dutch RD foreign firm 116,600 7/9/2002
3. Unilever NV UN foreign firm 37,628 7/9/2002
4. Alcan AL foreign firm 11,605 7/9/2002
5. Nortel Networks NT foreign firm 6,140 7/9/2002
6. Barrick Gold ABX foreign firm 9,900 7/9/2002
7. Placer Dome PDG foreign firm 3,600 7/9/2002
8. Inco Ltd. N foreign firm 4,065 7/9/2002
9. Immunex IMNX merger 7/12/2002
10. Conexant Systems CNXT spin-off 6/20/2002
11. WorldCom WCOM bankruptcy 5/13/2002
12. USAirways U bankruptcy 5/13/2002
13. Sapient SAPE 225 5/9/2002
14. Compaq CPQ merger 5/2/2002
15. Williamette Industries WLL merger 2/5/2002
16. Niagara Mohawk NMK merger 1/23/2002
17. Westvaco W merger 1/23/2002
18. Mead MEA merger 1/23/2002
19. Kmart KM bankruptcy 1/15/2002
All announcements are made after market close on the announcement date indicated in the
table. All changes become effective at the close on the effective date. Size is the market capi-
talization as of the day before announcement. Abnormal return is calculated as raw return
minus the S&P 500 return.
Number Abnormal Abnormal Abnormal Abnormal
Effective of Days Return Return Return Return
Date Between Return (AD+2 (ED+1 (ED+1
(ED) AD and ED (%) to ED) to ED+5) to ED+20)
7/24/2002 1 –22.5
5/10/2002 1 –11.7
Beyond the Random Walk190
an abnormal return, the limit price is adjusted at the end of each day
to reflect the movement in the S&P 500. The results are given below:
Price Effect Return
to be (to a short
Captured Date Bought Back position)
Stock (%) (days) (%)
UPS 20.7 Aug. 16, 2002 (20 days) 10.9
GS 22.5 Aug. 16, 2002 (20 days) 6.3
PRU 21.0 Aug. 16, 2002 (20 days) 11.0
EBAY 7.1 Jul. 31, 2002 (8 days) 7.1
PFG 9.8 Aug. 6, 2002 (12 days) 9.8
MI 3.9 Mar. 6, 2002 (17 days) 3.9
The total abnormal return from short-selling the added stocks is
8.2 percent over an average holding period of 16 days. Considering
transaction costs of 0.75 percent, slightly higher for short selling,
the net return is 7.5 percent. The annualized abnormal return is over
DELETIONS: SHORT-SELL ON ANNOUNCEMENT DATE
AND BUY BACK ON EFFECTIVE DATE
Unfortunately, there are no deletions that satisfy the criteria men-
tioned above. Only two firms are voluntarily deleted by Standard
and Poor’s: Conseco and Sapient.4
Both of them are low-price stocks.
Low-price stocks are especially risky because they could be delisted
from the exchanges, which is devastating for a stock; they could
reflect continuing problems with company’s business or other fac-
tors. For example, after being booted out of the S&P 500 on July 24,
2002, Conseco defaulted on debt payments and filed for bankruptcy
on August 8, 2002. On the other hand, Sapient gained 15.3 percent
in the week following exclusion from the index.
DELETIONS: BUY ON EFFECTIVE DATE AND
HOLD FOR UP TO TWENTY DAYS
Again, the sample of deletions is zero. The data in Tables 8.2 and 8.4
suggest that this strategy would have been profitable had qualify-
ing deletions been available.
Overall, the primary strategy for additions generated a return of
6.4 percent over 6.2 days; the secondary strategy for additions gen-
Changes to the S&P 500 Index 191
erated a return of 7.5 percent over 16 days. Both these strategies
were very successful. Unfortunately, no deletions met the criteria
The evidence presented in this chapter and the trading strategy rec-
ommendations rely on past data. Since future market conditions
and market patterns may change without notice, it is possible that
trading on S&P 500 index changes will cease to be profitable. Fur-
thermore, the analysis is based on abnormal returns, not raw re-
turns, which means that if the market is falling, investors may lose
money even though abnormal returns are positive.
In addition, the risk related to trading with index changes is not
explicitly considered. The risk can be reduced by hedging with the
S&P 500 index, and the results provided are actually based on the
assumption of hedging. The hedging will require short-selling the
S&P 500 index whenever a long position in the additions or dele-
tions is taken, and buying the S&P 500 index whenever a short po-
sition in the additions or deletions is taken.
• Firms are periodically deleted from the S&P 500 index because
of major restructuring or because they no longer represent the
U.S. economy. Each deletion is accompanied by an addition to
keep the number of firms in the S&P 500 constant at 500. There
are certain guidelines for changes made by Standard and Poor’s.
However, the process is largely subjective and unpredictable.
• Changes to the index are announced after the market closes
and become effective either on the next day or several days
later. Each change in the index is associated with a price effect
called the index effect. The index effect is usually positive for
additions and negative for deletions.
• The index effect has two components: temporary and perma-
nent. The temporary component of the index effect is concen-
trated around the effective date. While additions have both a
temporary and permanent effect, deletions have only a tempo-
rary effect. That is, firms deleted from the index usually regain
Beyond the Random Walk192
• The index effect persists because index fund managers are in-
tent on minimizing the tracking error (difference between the
fund return and the S&P 500 index return). Therefore, they must
buy added stocks and sell deleted stocks as close to the close
on the effective date as possible, irrespective of whether they
are paying more or receiving less. Other market participants
know this and can trade to take advantage of the index funds.
• While the temporary effect occurs around the effective date and
can be captured by arbitrageurs, the permanent effect occurs
only for additions and cannot be captured through arbitrage.
• The four possible trading strategies (two each for deletions and
additions) consist of two short sales and two purchases. For
additions, an investor would buy the added stock after the
announcement and sell on the effective date. Second, the in-
vestor would short-sell the added firm after it has been added
and repurchase it up to twenty days later. For deletions, the
first strategy is to short-sell immediately after the announce-
ment and cover on the effective date. The second strategy is to
buy after the stock has been deleted from the index and sell up
to twenty days later.
• The trading strategies are tested with index changes that oc-
curred between January 2002 and July 2002. Both trading strat-
egies for additions are successful, generating 6.9 percent over
6.2 days and 8.2 percent over 16 days. Unfortunately, no dele-
tions qualify for a trading strategy during this period.
Changes to the S&P 500 index are not predictable. However, there is
a pattern in prices after the changes to the index are announced. It is
possible to capture the temporary index effect for both additions
and deletions. The anticipated annualized abnormal return is be-
tween 15 percent and 25 percent.
Information About Index Changes
http://www.spglobal.com: Standard and Poor’s issues a press release and
posts it on its website. In addition, all major news services carry the news.
Changes to the S&P 500 Index 193
SEC Filings for Accessing Annual Reports
http://www.secinfo.com: There are many sources for SEC filings. This is
among the best. Go to Item 5 in the annual report to get the number of
http://www.sec.gov/edgar/searchedgar/companysearch.html: This SEC site
has all of the filings. But it is sometimes difficult to navigate.
http://www.freeedgar.com: This site collates information from the SEC’s
EDGAR database and makes it available in a more accessible format. The
information is limited but free.
http://www.edgar-online.com: This site is good but is only accessible by
paying users. To bypass the authorization, enter through http://
finance.yahoo.com by clicking on SEC filings under the quotation for a
Sources for Intraday Stock Data
Companies and brokerage firms that provide real time quotes also allow access
to capture time and sales data for selected stocks. However, it is usually not pos-
sible to get historical tick by tick data. Historical data are available from the fol-
http://www.tickdata.com: Tickdata has data for several hundred large compa-
nies for the past few years. In addition, they also sell futures price data.
Their software is very useful for those uninitiated in handling large data sets
and statistical packages. However, they are very expensive, and their
customer service is poor.
http://www.nysedata.com: Look under Data Products, Stock Prices, and then
Historical. The New York Stock Exchange’s Trade and Quote database (TAQ)
provides tick-by-tick data for all stocks (NYSE, AMEX, and Nasdaq) on CD
from 1993. The cost is $500 per month for all stocks.
http://www.interquote.com: A data service provider. However, the investor is
responsible for downloading, storing, and analyzing the data.
References for Further Reading
Arbel, Avner. 1985. Generic Stocks: The Key to Market Anomalies. Journal of Port-
folio Management 11(4), 4–13.
Arbel, Avner, and Paul Strebel. 1982. The Neglected and Small Firm Effects. Fi-
nancial Review 17(4), 201–18.
Beneish, Messod D., and Robert E. Whaley. 1996. An Anatomy of the “S&P 500
Game”: The Effects of Changing the Rules. Journal of Finance 51(5), 1909–30.
——— . 2002. S&P 500 Index Replacements: A New Game in Town. The Journal of
Portfolio Management, fall, 51–60.
Blouin, Jennifer, Jana Raedy, and Douglas Shackelford. 2000. The Impact of Capi-
tal Gains Taxes on Stock Price Reactions to S&P 500 Inclusion. NBER working
Blume, Marshall, and Roger Edelen. 2003. On S&P 500 Index Replication Strate-
gies. Working paper, Department of Finance, Wharton School, University of
Bos, Roger. 2000. Quantifying the Effect of Being Added to an S&P Index. Stan-
dard and Poor’s report, September.
Beyond the Random Walk194
Chan, Louis K. C., Narasimhan Jegadeesh, and Josef Lakonishok. 1995. Evaluat-
ing the Performance of Value Versus Glamour Stocks: The Impact of Selection
Bias. Journal of Financial Economics 38(3), 269–96.
Chen, Honghui, Greg Noronha, and Vijay Singal. 2004. The Price Response to
S&P 500 Index Additions and Deletions: Evidence of Asymmetry and a New
Explanation. Forthcoming in the Journal of Finance.
Chordia, Tarun. 2001. Liquidity and Returns: The Impact of Inclusion into the
S&P 500 Index. Working paper, Department of Finance, Emory University.
Coval, Joshua D., and Tobias J. Moskowitz. 1999. Home Bias at Home: Local Eq-
uity Preference in Domestic Portfolios. Journal of Finance 54(6), 2045–73.
Dash, Srikant. 2002. Price Changes Associated with S&P 500 Deletions. Standard
and Poor’s report, July.
Denis, Diane, John McConnell, Alexei Ovtchinnikov, and Yun Yu. 2003. S&P 500
Index Additions and Earnings Expectations. Journal of Finance, forthcoming.
Dhillon, Upinder, and Herb Johnson. 1991. Changes in the Standard and Poor’s
500 List. Journal of Business 64(1), 75–86.
Elliott, William B., and Richard S. Warr. 2003. Price Pressure on the NYSE and
NASDAQ: Evidence from S&P 500 Index Changes. Financial Management, forth-
Goetzmann, William N., and Mark Garry. 1986. Does Delisting from the S&P 500
Affect Stock Price? Financial Analyst Journal 42(2), 64–69.
Gosnell, Thomas, and Timothy Krehbiel. 2000. Market Liquidity and Changes in
the Roster of the Standard and Poor’s 500 Index. Working paper, Department
of Finance, Oklahoma State University.
Harris, Lawrence, and Eitan Gurel. 1986. Price and Volume Effects Associated
with Changes in the S&P 500: New Evidence for the Existence of Price Pres-
sures. Journal of Finance 41(4), 815–30.
Hegde, Shantaram, and John McDermott. 2003. The Liquidity Effects of Revisions
to the S&P 500 Index: An Empirical Analysis. Journal of Financial Markets 6(3):
Jain, Prem C. 1987. The Effect on Stock Price of Inclusion in or Exclusion from the
S&P 500. Financial Analyst Journal 43(1), 58–65.
Kaul,Aditya, Vikas Mehrotra, and Randall Morck. 2000. Demand Curves for Stocks
Do Slope Down: New Evidence from an Index Weights Adjustment. Journal of
Finance 55(2), 893–912.
Lynch, Anthony W., and Richard R. Mendenhall. 1997. New Evidence on Stock
Price Effects Associated with Changes in the S&P 500 Index. Journal of Business
Merton, Robert C. 1987. Presidential Address: A Simple Model of Capital Market
Equilibrium with Incomplete Information. Journal of Finance 42(3), 483–510.
Pruitt, Stephen W., and K. C. John Wei. 1989. Institutional Ownership and Changes
in the S&P 500. Journal of Finance 44(2), 509–14.
Shleifer, Andrei. 1986. Do Demand Curves for Stocks Slope Down? Journal of Fi-
nance 41(3), 579–90.
Subrahmanyam, Avanidhar, and Sheridan Titman. 2001. Feedback from Stock
Prices to Cash Flows. Journal of Finance 56(6), 2389–413.
Wurgler, Jeffrey, and Ekaterina Zhuravskaya. 2002. Does Arbitrage Flatten De-
mand Curves for Stocks. Journal of Business 75(4), 583–608.
Changes to the S&P 500 Index 195
1. This chapter is based on research by the author with Honghui Chen and Greg
Noronha (2003) in “The Price Response to S&P 500 Index Additions and De-
letions.” Other work used in this chapter includes Arbel and Strebel (1982),
Beneish and Whaley (1996, 2002), Blouin, Raedy, and Shackelford (2000),
Blume and Edelen (2003), Chordia (2001), Coval and Moskowitz (1999), Denis
et al. (2003), Dhillon and Johnson (1991), Elliott and Warr (2003), Goetzmann
and Garry (1986), Gosnell and Krehbiel (2000), Harris and Gurel (1986), Hegde
and McDermott (2003), Jain (1987), Kaul, Mehrotra, and Morck (2000), Lynch
and Mendenhall (1997), Merton (1987), Pruitt and Wei (1989), Shleifer (1986),
and Wurgler and Zhuravskaya (2002).
2. There are exceptions. Occasionally an involuntary deletion takes place be-
fore a suitable replacement is found.
3. The value of assets that track the S&P 500 index is about $1 trillion, and the
total market value of all U.S. stocks is $12 trillion; dividing the second figure
into the first gives a figure of about 8 percent.
4. Foreign firms are not considered because they operate in a different environ-
ment. Moreover, none of the evidence presented above includes deletion of
any foreign companies.
Beyond the Random Walk196
When a merger is announced, the target’s price should rise close to the
bidder’s offer for the target. However, in most cases it does not. Two
reasons account for the difference. First, successful completion of the
merger is not a certainty. Second, shareholders of the target firm must
earn a positive return until consummation of the merger, which implies
that the target’s price must be less than the offered price. Based on past
completion rates and completion periods, the difference in the bidder’s
offer and the actual target price after merger announcement is larger
than what it should be.
Investors and arbitrageurs can earn annual abnormal returns of 4 to
10 percent by buying the target upon a cash merger announcement,
and by buying the target and short-selling the bidder upon announce-
ment of a stock merger. The profitability of merger arbitrage can be
improved by carefully selecting mergers in which large arbitrageurs are
unlikely to participate but which generate higher abnormal returns.
Though merger arbitrage or risk arbitrage is used extensively by
institutions and sophisticated investors, it is not frequently discussed
in the media.1
The first major public disclosure of merger arbitrage
was made by Ivan Boesky in his 1985 book Merger Mania—Arbi-
trage: Wall Street’s Best Kept Money-Making Secret, though a couple
of stories had run in the popular press.2
The purpose of merger ar-
bitrage is to take advantage of a mispricing that might occur after
the intended merger has been announced. This activity is perfectly
legal. On the other hand, trading before merger announcement based
Merger Arbitrage 197
on nonpublic information is illegal (see Chapter 7). Ivan Boesky, a
well-known takeover speculator, became famous in the mid-1980s
when he was charged by the Securities and Exchange Commission
for insider trading related to mergers. Later, he was convicted and
fined $100 million and sentenced to three years in jail.
THE MERGER PROCESS AND MERGER GAINS
A merger, also called a takeover or acquisition, occurs when one
company buys another company. The steps in the merger process
are initiation of merger discussions by one of the two parties, agree-
ment to merge by the boards of the two companies, approval by
any regulatory bodies pertinent to the merger, and approval by the
stockholders of the two companies. Sometimes the boards of direc-
tors may not agree to a merger. In those cases, the acquiring com-
pany can commence a hostile tender offer (that is, directly approach
the stockholders to tender their shares to the acquiring firm), by-
passing the management of the company. Hostile bids were more
common in the 1980s than in the 1970s or the 1990s. Hostile bids
constituted about 8 percent of all bids during 1973–79, 14 percent
during 1980–89, and 4 percent during 1990–98.
Firms merge because, in general, mergers create value by gener-
ating synergistic gains. Synergies may arise due to improvement in
efficiency or enhancement of market power. The combined abnor-
mal return to the target and acquirer around announcement is about
2 percent of the combined size. However, nearly all of the gain ac-
crues to the target firm (about 16 percent of the target firm’s size),
whereas the acquiring firm gains nothing or loses due to the merger.
Several explanations are offered for the poor performance of
acquirers and why acquirers choose to merge in spite of negligible
gains. These are discussed in the references listed for this chapter.
MODE OF PAYMENT IN MERGERS
The mode of payment (primarily cash or stock) for the target is im-
portant for merger arbitrage because it affects the division of gains
between the target and the bidder and conveys information about
the value of the bidder. During the 1990–98 period, 28 percent of the
mergers were all-cash deals and 58 percent were all-stock deals. Dur-
ing the 1970s and 1980s, however, the fraction of cash deals was greater
than that of stock deals. In terms of division of gains, bidders tend to
lose about 2 percent when they pay for the merger in stock, whereas
the announcement return to the bidder is near zero when bidders use
cash to pay for the merger. Targets gain 13 percent with a stock deal
Beyond the Random Walk198
and 20 percent with a cash deal. The difference in merger gains de-
pending on the mode of payment has been explained by theoretical
models based on differences in information available to investors
and the management. One model suggests that the market assumes
bidder equity is overpriced when bidders use stock to pay for an
acquisition; a second model suggests risk sharing by target share-
holders with a stock bid; a third one asserts that low-valued bid-
ders pay for a merger using stock; yet another believes that a cash
bid implies a higher valuation of the target than a stock bid.
Why do bidders pay stock or targets accept stock as a form of
payment given the negative implications of a stock bid? Bidders
like to pay with stock because as the value of the target firm to the
bidder changes depending on market conditions, so does the price
paid by the bidder in stock. If, on the other hand, the bidder makes
a cash bid, then that amount doesn’t change based on the bidder’s
ability to pay, or on whether the economy or the company’s indus-
try takes a downturn. Target shareholders are in a quandary. They
prefer a stock payment because of tax implications but would like
to receive cash because there is no uncertainty about the amount of
money. As an example, consider the AOL–Time Warner merger,
where AOL agreed to pay 1.5 shares of its stock for each share of
Time Warner stock. AOL’s price before announcement of the bid
was $73 per share. With a 1.5 share ratio, Time Warner shareholders
expect to receive $109.50 for each share. If AOL’s stock price fell to
$35, Time Warner shareholders would receive only $52.50, intro-
ducing uncertainty into the amount received by the target firm.
Collars are a recent innovation, a way of partially addressing both
bidder and target concerns. When a collar is used, the bidding firm
uses its stock to buy the target firm. However, the collar stipulates
that if the bidder’s stock drops (rises) to a certain level, then the
number of shares that the bidding firm would give to the target
firm is increased (reduced). There are many versions of a collar, but
the most common is one where it is a fixed-price offer (payable in
stock) if the stock price stays within predefined bounds. Outside
that range, the offer becomes strictly a stock offer whose value
changes with the bidder’s stock price. For example, MCI
WorldCom’s aborted $115 billion bid for Sprint in October 1999 was
structured as a stock bid with a collar as follows:
WorldCom’s stock price Number of bidder shares per target share
$0 to $62.15 1.2228 WorldCom shares per Sprint share
$62.15 to $80.85 Variable, such that the payment is $76 per
Over $80.85 0.94 WorldCom shares per Sprint share
Merger Arbitrage 199
It is a fixed-price offer of $76 if WorldCom’s price stays between
$62.15 and $80.85. Otherwise, it becomes a typical stock offer.
Thus, collars make the amount payable to target shareholders
more certain and make the bid look a little more like a cash transac-
tion rather than a purely stock transaction. On the other hand, a big
change in the stock price makes the bid appear more like a stock bid
but with less risk for the bidding firm than a purely stock transac-
tion. Researchers have found that the market does not penalize the
bidding firm for using stock in conjunction with a collar; rather, the
market interprets the use of a collar as a signal that the bidder’s
stock is currently not overvalued.
When a merger between two firms is announced, the stock price of
the target firm may remain below the level promised by the bid-
ding firm. The difference between the target’s price and the bidder’s
offer price is referred to as the speculation spread. The idea is to cap-
ture the speculation spread in an efficient and selective manner. In
the subsections below, the merger arbitrage process is considered
for stock mergers, cash mergers, mergers with collars, and mergers
where multiple bids are made for the same target.
STOCK MERGERS—SINGLE BID
When the target’s stock price does not rise to the bidder’s offer, trad-
ers can make arbitrage profits by strategic execution. An all-stock
merger such as America Online’s (NYSE: AOL) acquisition of Time
Warner (NYSE: TWX) is a good example. The merger was announced
after the close on January 7, 2000 (a Friday). AOL agreed to pay 1.5
shares for each share of Time Warner. On the next trading day (Janu-
ary 10, 2000),AOLclosed at $71.88 and Time Warner closed at $90.06.
Based onAOL’s offer of 1.5 shares and it’s closing price, Time Warner
should have closed at $107.82. The speculation spread in this case is
$17.76 ($107.82—$90.06), or 19.7 percent. An arbitrageur could buy
one share of Time Warner at $90.06 (pays $90.06) and short-sell 1.5
shares ofAmerica Online at $71.88 (receives $107.82). The arbitrageur
has no risk in this position, assuming successful completion of the
merger on these terms. If AOL’s price rises, the short position in AOL
loses but the long position in TWX gains an equivalent amount. If
AOL’s price falls, the short position gains and the long position in
Beyond the Random Walk200
TWX loses. In addition, if there are zero transactions costs and the
merger completion is immediate, then the arbitrageur makes a
riskless profit of almost 20 percent with zero investment. Everyone
would want to earn profits of this magnitude.
Obviously, the completion cannot be immediate. The AOL–Time
Warner merger was completed on January 11, 2001—almost exactly
one year later. The price of Time Warner had fallen to $71.19 but
was 1.5 times AOL’s price for that day, allowing the trader to close
out both positions. Our arbitrageur would have earned a low-risk
profit of 20 percent in one year—pretty good, considering that the
S&P 500 lost about 10 percent during that period.
In addition to the time delay, there is uncertainty about the comple-
tion of the merger. If the merger is unsuccessful, then the loss to the
arbitrageur can be substantial. The target firm’s stock would lose
the premium promised by the bidder and more, because the target
firm has definitely lost time and energy in pursuing the merger. On
the other hand, the bidder firm’s stock might even rise due to relief
on part of the bidder stockholders (recall that the bidding firms usu-
ally do not gain upon announcement of a merger). The aborted
merger of General Electric (GE) and Honeywell is a good example.
GE offered 1.055 of its shares for each share of Honeywell after the
close of trading on October 20, 2000. GE’s stock closed at $49.75 on
the next trading day, while Honeywell’s stock closed at $49.94. Since
Honeywell’s stock price is higher than GE’s price by only 0.4 per-
cent instead of 5.5 percent, the speculation spread is 5.1 percent. On
June 14, 2001, it became clear that the GE-Honeywell merger would
not go through, as the demands made by the European Union were
too onerous for GE to accept. At the close of trading that day,
Honeywell’s price was $37.10 compared with GE’s price of $48.86.
Instead of making a profit of 5 percent, the arbitrageur would have
lost 25 percent, not counting transaction costs.
The above examples illustrate the two primary reasons for the
speculation spread: risk of failure and delay in completion of the
merger. Several factors affect the probability of failure: the chance
that the merger will not be approved by the local government, for-
eign government, target firm’s stockholders, or bidder firm’s stock-
holders; the delay in obtaining those approvals; and the operation
of certain force majeure clauses (poor performance, fraud, severe
industry or economic downturn, etc.) that preclude the completion
of the merger. Besides the risk of failure and time delay, arbitrageurs
must consider the difficulty and the significantly higher cost and
risk of short selling.3
Merger Arbitrage 201
CASH MERGERS—SINGLE BID
The process for cash mergers is the same as for stock mergers ex-
cept that the cash offered by the bidder is independent of the bidder’s
stock price. Thus, the arbitrageur’s job is much simpler: buy the
target, and there is no need to short-sell the bidder’s stock. Take the
example of Medtronic’s $48 cash bid for MiniMed that was an-
nounced on May 30, 2001, before the market opened. MiniMed closed
at $46.77 that day. An arbitrageur could have bought MiniMed at
$46.77 and held it until completion of the merger. By the time of
merger completion on August 28, 2001, MiniMed’s price had risen
to $47.99, giving a return of 2.6 percent over a three-month period,
which is equivalent to an annualized return of approximately 11
As mentioned above, the fraction of cash deals is much smaller
than the fraction of stock deals. Moreover, the targets are generally
much smaller than the acquiring firms in cash deals. Due to the
relative size and greater certainty for target stockholders, cash deals
should have a higher probability of success. However, the evidence
reported in the next section shows that cash deals do not necessar-
ily have a greater probability of success.
MERGERS WITH COLLARS—SINGLE BID
As explained in the previous section, mergers with collars are like
cash mergers or stock mergers, depending on the bidder’s stock
price. Broadly, the strategy is to buy shares of the target firm upon
announcement without a corresponding short sale in the acquiring
firm. However, if the bidder’s stock price begins to fall and it seems
as though the collar will be triggered, then the position in the target
should be protected by short-selling the bidder’s stock. Mergers with
collars are usually somewhat complex and require close oversight.
MERGERS WITH MULTIPLE BIDS
A merger need not take place just with a single bid for the target.
About 20 percent of mergers have multiple bids. When another bid
from the same bidder or a new competing bidder is expected, the
stock price of the target firm may rise above the initial bid. For ex-
ample, Sabre Holdings made a cash offer of $23 for Travelocity on
February 19, 2002, at a premium of 20 percent over Travelocity’s
previous day’s closing price of $19.20. However, Travelocity jumped
to $24.91 in anticipation of higher bids. On March 18, 2002, Sabre
Holdings sweetened its offer to $28 and Travelocity’s price held at
Beyond the Random Walk202
$27.97 on that date, with the market participants expecting that the
deal would be completed at that price. The merger was completed
on April 11, 2002.
Bidding contests can be much longer and more complex than
Sabre’s acquisition of Travelocity. Northrop Grumman’s initial bid
for TRW on the morning of February 22, 2002, was $47 in cash, a
premium of 18 percent. However, TRW soared to $50.30 by the end
of the day, indicating that another bid (or bidder) would be forth-
coming. On April 15, 2002, Northrop raised the bid to $53, and then
to $58 on June 25, 2002. In the meantime, several firms expressed
interest in different business segments of TRW. Finally Northrop
agreed to buy TRW for $60 on July 1, 2002, an offer that was ac-
cepted by TRW. As you can observe, multiple bids are rewarding
for arbitrageurs who take positions after the first bid. This is borne
out by the evidence in the next section.
Table 9.1 summarizes the abnormal returns from merger arbitrage.
The return is calculated assuming that the target firm’s stock is pur-
chased at the end of the first trading day after the announcement
and sold upon merger completion or upon withdrawal of the offer
by the bidder. In the case of stock mergers, shares of the acquiring
firm are short-sold in the correct proportion and the position is liq-
uidated upon merger completion or upon withdrawal of the offer.
This is the raw return earned from merger arbitrage. The abnormal
return is obtained after adjusting for return commensurate with this
kind of risk. If the risk is assumed to be zero, then the abnormal
return is simply the raw return minus the risk free rate. If risk is
assumed to be market risk, then the abnormal return is the raw re-
turn minus the market return. The systematic risk in the case of
merger arbitrage is usually less than the market risk because the
risk of failure of the merger depends on many factors besides stock
In Table 9.1, annualized returns are reported for a better under-
standing of the magnitude of gains. To annualize the abnormal re-
turn, it is assumed that the same return can be earned for multiple
mergers sequentially. For example, if an abnormal return of 5 per-
cent is earned over a two-month period from merger announce-
ment to merger completion, it is assumed that we will earn the same
5 percent abnormal return in a sequence of six merger arbitrage deals.
Thus, the annualized return is calculated simply as the 5 percent
Table 9.1 Returns to Merger Arbitrage
Days to Annual- Annual-
Complet- ized ized
First Percent Failure tion or aw Abnormal
Sample Sample Offers Cash Ratea
With- Return Return Special
Study Period Size Only (%) (%) drawal (%) (%) Notes Source
1. 1997 37 Yes 100 14 57.3 52.3 33.9 Only Canadian Karolyi and
mergers Shannon (1999)
2. 1981–1995 362 Yes 100 3 72 46.5 24b
3. 1981–1996 1,901 No 70 16 NA 18.5 9.6 Pure cash Baker and
or pure stock Savasoglu
4. 1963-1998 4,750 No 73 15 59.3 10.6 4 Accounts for Mitchell and
various kinds Pulvino (2001)
of costs and risk
The failure rate is defined as the percent of targets that remain independent.
Not reported in the study. Author’s estimate.
Beyond the Random Walk204
abnormal return times six. This corresponds to the “Annualized
Abnormal Return” column.
The failure rate represents the percentage of targets that remain
independent. The percentage of unsuccessful bids will be higher
than the figure listed here because some targets have multiple bids
and only one of those bids can be successful.
It is interesting to note from Table 9.1 that all studies, without
exception, report positive abnormal returns for merger arbitrage after
controlling for risk. However, the annualized abnormal return var-
ies from a low of 4 percent to a high of 33.9 percent. Four studies
have investigated different aspects of merger arbitrage, and a dis-
cussion of the individual studies is instructive in highlighting and
understanding various facets of merger arbitrage.
The first study in Table 9.1 shows that the average merger arbitrage
spread in thirty-seven Canadian cash deals that took place in 1997
and were valued at more than C $50 million each is 7.81 percent.
Considering an average duration of 57.3 days, this translates into
52.3 percent annually. Only five deals out of thirty-seven (14 per-
cent) generated zero or negative returns, while 30 percent gener-
ated more than 10 percent. Making a naive adjustment for risk based
on the Toronto Stock Exchange 300 index generates an annual ab-
normal return of 33.9 percent. However, the actual risk levels are
lower: the average preannouncement-period beta risk for the tar-
gets is 0.52, while the “in-play” beta is lower at 0.39. As the beta risk
for the Toronto Stock Exchange is close to 1, it would seem that the
risk adjustment is generous.
A similar but broader study of 362 cash mergers during 1981–95
that were valued at more than $10 million (see Table 9.2 below) gives
the following main results based on the first bid for a target:
A 97 percent completion rate suggests that the risk of failure is
relatively small in cash offers. In addition, offers are revised up-
ward in 39 percent of the cases and revised down in only 4 percent
of the cases. The revision in offers has a considerable impact and
accounts for much of the returns. The revision return is 6.9 percent,
whereas the arbitrage spread is only 1.9 percent. Indeed, a negative
arbitrage spread suggests the likelihood of additional bidders or
the first bidder upping its bid. Sabre’s bid for Travelocity and
Northrop’s bid for TRW are examples of upward revisions.
The average lead time, from announcement to completion or with-
drawal, is seventy-two days. A majority of the offers (62 percent) are
Merger Arbitrage 205
completed within two months, and only 6 percent last more than six
months. A total of 7.5 percent of the deals result in negative returns.
Based on the average duration of seventy-two days, the annualized
raw return is 46.5 percent. Adjustment for risk results in a return of
2.0 percent per month, or approximately 24 percent annually.
CASH AND STOCK MERGERS
The remaining two studies examine samples of both cash and stock
mergers. The first study consists of 1,901 cash and stock merger
offers during 1981–96. The definition of a cash deal is a fixed-price
deal whether the consideration is paid in stock or cash. The 1,901
offers have only 1,556 targets. The remaining 345 offers are revised
or new bids for the same target. Overall, 30 percent of the offers are
stock deals. However, the fraction of stock deals increases substan-
tially over time, from 19 percent in the pre-1990 period to 44 percent
thereafter. In the sample, 16.3 percent of the targets remain inde-
pendent, while 22.7 percent of the deals fail.
Targets of cash offers are bought upon announcement. No stake
is taken in the bidder firm. In the case of stock offers, however, the
bidder firm is short-sold in addition to buying the target firm. Be-
sides adding stock mergers to the sample, this study computes ab-
normal returns based on sequential availability of merger deals. If
no merger deals are available in a particular period, then the abnor-
mal return for that period is zero. Based on these considerations,
the raw return to an arbitrage portfolio is 1.5 percent per month for
all offers. If only the first offer is considered, then the return is 1.6
Table 9.2 Cash Mergers Valued at More than $10 Million, 1981–1995
Completed 350 (97%)
Withdrawn 12 (3%)
Total sample 362 (100%)
Revised up 140 (39%)
Revised down 15 (4%)
Unrevised 207 (57%)
Total sample 362 (100%)
Returns Mean Minimum Median Maximum % Negative
Arbitrage spread 1.9% –30.1% 2.0% 41.5% 23.1%
Revision return 6.9% –55.6% 0.0% 101.5% 4.1%
Total 8.8% –51.9% 3.3% 91.0% 7.5%
Period (days) 72 14 48 565
Beyond the Random Walk206
percent per month. By comparison, the market earns 1.2 percent
per month, and the risk-free rate is 0.6 percent per month. Adjusted
for risk, the excess return is about 0.8 percent per month or 9.6 per-
The other study of cash and stock mergers has the largest sample
of bids (4,750 offers) over the longest period (1963–98). The sample
includes both pure cash and pure stock bids, and bids that seek less
than 100 percent of the target as long as the acquisition will result in
the acquirer holding the entire 100 percent. For example, a com-
pany holding 75 percent of the target may seek to acquire the re-
maining 25 percent through a merger or a tender offer. For this
sample of merger arbitrage deals, the risk-adjusted return is 0.7 per-
cent per month if transaction costs and other slippages are not con-
sidered. The risk-adjusted return falls to 0.3 percent per month if all
impediments and costs of transacting are considered. Further, the
risk of the arbitrage portfolio is close to zero in stable or appreciat-
ing markets, but the systematic risk as measured by beta jumps to
0.50 in downtrending markets. Some other interesting information
relating to the success of merger arbitrage is given in Table 9.3.4
Table 9.3 Success of Merger Arbitrage
Hostile Deals Cash Deals Stock Deals
Total number of first bids 3,434 1,815 475
Arbitrageur loses money 778 (23%) 356 (20%) 143 (30%)
First bid fails 606 (18%) 295 (16%) 173 (36%)
Target not bought out 478 (14%) 272 (15%) 131 (28%)
Targets taken over 86% 85% 72%
It can be observed that the failure rate is high in the case of hos-
tile deals. Also, stock deals are slightly more successful than cash
deals. Further, the chance that the target will remain independent is
only 14–15 percent.
Overall, the evidence presented in Tables 9.1 to 9.3 suggests that
there is indisputable proof of positive abnormal returns from merger
arbitrage. The excess returns to merger arbitrage vary between 4
percent and 33.9 percent.
Factors in Determination of Profits
To optimize the gains from merger arbitrage, it is necessary to pre-
dict which offers are likely to provide maximum gains. There are
Merger Arbitrage 207
three main factors that affect the magnitude of arbitrage profits:
probability of success, time from announcement to completion or
withdrawal, and arbitrage activity. Arbitrage activity can directly
influence the spread, and all three factors are interrelated.
PROBABILITY OF MERGER SUCCESS
First, consider the probability that an announced merger will be
successful. The greater the chance of success, the greater the ex-
pected profit. And if the chance of success is 100 percent, then the
profit is risk-free. This also implies that the greater the probability
of success, the larger the number of investors and other arbitrageurs,
and therefore a smaller merger arbitrage spread. Thus, a greater
probability of success is accompanied by a smaller speculation
spread. On the other hand, if investors assign a low probability of
success to a merger, fewer investors will participate in the merger
leading to a high speculation spread. It is, therefore, easy to judge
the likelihood of success given the speculation spread. In general,
mergers with high initial spreads are less likely to succeed. Studies
have found that the average arbitrage spread is high (average > 15
percent) for failed deals but less than 10 percent for successful deals.
Besides what can be gleaned from the arbitrage spread, the prob-
ability of success depends on the characteristics of the deal. These
are listed in Table 9.4. Managerial resistance seems to be the most
important, and a decisive deterrent to success. However, there are
large differences in the reported success of hostile bids. The prob-
ability of success is estimated to fall by anywhere from 4 percent to
45 percent for hostile bids compared to friendly bids. From Table
9.3 it can be seen that 72 percent of the targets that are subject to
hostile bids are eventually taken over. Indeed, this is lower than the
85 percent of targets eventually acquired in the overall sample.
However, the price of success is sweet. There is a very high likeli-
hood that the hostile bid will be revised upward to induce the man-
agement to change its mind, giving much higher returns to the
The probability of success also depends on market conditions. If
there is a downturn in market conditions, then the bidder is not as
keen to acquire the target because of the uncertain nature of the
economy. It may also have a difficult time securing funds to buy the
target. In a stock deal, the bidder is somewhat protected because a
fall in its stock price (due to the market downturn) also reduces the
price it pays for the target, and the bidder does not need external
funds to finance the acquisition. However, in a cash deal, the price
Table 9.4 Effect on Arbitrage Profits
on Probability of
Success, Duration Evidence Against
Factor and Arbitrage Activity Support for the Prediction the Prediction
Managerial resistance Reduces the probability of Walkling (1985), Schwert (2000),
(hostile bid) success; increases duration Baker and Savasoglu (2002),
Jindra and Walkling (2001),
Mitchell and Pulvino (2001)
Falling stock market Reduces the probability of success Mitchell and Pulvino (2001)
Cash deal Reduces the probability of success Mitchell and Pulvino (2001) No effect—Baker and
Large targets Reduces the probability of success; Baker and Savasoglu (2002), No effect—Mitchell and
reduces arbitrage activity Jindra and Walkling (2001) Pulvino (2001)
Large acquirers Increases the probability of success Baker and Savasoglu (2002) No effect—Mitchell and
Takeover premium Increases the probability of success Fishman (1988)—theory No effect—Baker and
Mitchell and Pulvino (2001)
Bidder and target in Reduces the probability of success; No effect—Baker and
the same industry increases duration Savasoglu (2002)
Low stock price, low Reduces arbitrage activity Cornelli and Li (2002)—theory;
market capitalization, Jindra and Walkling (2001)
high merger activity,
or low turnover volume
High pre-bid runup or High arbitrage activity Cornelli and Li (2002)—theory;
highly abnormal Jindra and Walkling (2001)
Merger Arbitrage 209
of the target remains unchanged and the bidder may need external
financing. Therefore, there is a greater likelihood for the merger to
fail. A 5 percent decrease in contemporaneous or lagged monthly
market return increases the probability of failure by 2.25 percent.
There is also some evidence to suggest that there is no difference in
the probability of success between cash and stock offers. In addi-
tion, target size and bidder size do not seem to be important factors,
though financing for the merger and possible antitrust challenges
should be of concern. Higher takeover premium (price paid by the
bidder above the premerger price of the target) should increase the
probability of success, as the management and the stockholders of
the target firm will be more sympathetic to a higher bid. However,
none of the studies cited in Table 9.1 finds any effect of the takeover
premium on the chance of success.
It would seem that if the bidder and target firms are in the same
industry, then they are more likely to be subject to scrutiny for anti-
trust concerns, which would reduce the probability of success. How-
ever, there is no evidence to support that prediction either. Perhaps
the merging firms evaluate the probability of an antitrust contest
and desist from engaging in mergers that would raise serious ob-
jections from governmental authorities.
TIME TO MERGER COMPLETION
The second factor that affects arbitrage returns is the time for comple-
tion of the deal. If the expected time of completion is long, the arbi-
trage spread will be larger. Further, the longer the completion time,
the lower the probability of success. The time of merger completion
is likely to increase with managerial resistance and antitrust con-
cerns. In addition, management holdings will have a significant
impact. If the management holds a large stake in the firm, then it
can be instrumental in accepting or rejecting the bid.
The role of arbitrageurs is important in merger arbitrage. They can
become instrumental in the success or failure of a merger because
they are more willing to trade their shares than individual share-
holders or the management. If arbitrageurs are very interested in a
merger (due to potential arbitrage gains), then they will step in and
take large positions, which they will surrender at the appropriate time.
Thus, the greater the arbitrageur interest, the greater the probabil-
ity of success. Realizing the link between arbitrageur interest and
Beyond the Random Walk210
the probability of success, arbitrageurs tend to have a herd mental-
ity. However, this mentality is tempered by the size of profits: the
greater the arbitrageur interest, the smaller the profit. Therefore,
arbitrageurs would like to hide their trades to discourage other
arbitraguers and consequently earn higher profits.
Holding all else constant, arbitrage activity has three implications
for arbitrage profits. Since arbitrageurs are interested in hiding their
trades, they will invest in targets where volume turnover (daily
volume divided by the number of shares outstanding) is high. On
the other hand, targets with low volume turnover will experience
relatively low arbitrage activity and higher profits. Second,
arbitrageurs are unlikely to invest in low-price stocks (less than $5)
because those stocks are not marginable and, therefore, require a
larger capital outlay. Moreover, as low-price stocks are generally
low-market-capitalization stocks, they will have higher transaction
costs and a larger price impact due to large trades. Third, assuming
that capital available to arbitrageurs is limited, arbitrageurs must
choose among various merger deals. The capital constraint means
that arbitrageurs can’t take large positions in large targets because
of limited capital. In addition, in times of high merger activity,
arbitrageurs’ capital availability will act as a constraint. Thus, a pe-
riod of high merger activity is particularly good for earning high
The evidence above suggests that to earn high arbitrage profits,
investors should concentrate on small-size targets with low volume
and low price, in times of enhanced merger activity, and where there is
The persistence of abnormal returns in a variety of studies indicates
that the abnormal returns are real. There are three potential expla-
nations. If the cost of transacting is high, then the documented re-
turns may be unattainable. Further, annualizing short-period returns
can result in large returns that cannot be realistically obtained. For
example, if the AOL–Time Warner merger was consummated in ten
days instead of one year, then the ten-day return would have been
20 percent and the annualized return more than 700 percent. It is
difficult to repeat such high-yield events. Nonetheless, all of the
studies in Table 9.1 explicitly account for transaction costs. Even with
conservative assumptions, the minimum annual abnormal return
Merger Arbitrage 211
is 4 percent. With less conservative and more realistic assumptions,
the abnormal return is about 10 percent per year.
The second explanation relates to accounting for risk. Using his-
torical risk measures are never appropriate for event-driven returns
because the volatility (or risk) is unusually high around events.
However, risk around mergers is different. Since the position of the
arbitrageur is essentially hedged (except against a withdrawal), the
risk of merger arbitrage is rather low. The systematic (market-re-
lated) risk is close to zero in most instances except in downtrending
markets. Even in those cases, the beta of a merger arbitrage portfo-
lio is only one-half of the market portfolio. The Merger Fund (see
Table 9.5 below) estimates that its beta is less than 0.20. Nonethe-
less, accounting for risk is necessary. As noted in Table 9.1, all stud-
ies explicitly account for risk but still generate abnormal returns.
The third explanation refers to the limited capacity and risk-tak-
ing ability of the arbitrageurs. Arbitrageurs have limited access to
capital and would like to take positions that generate the highest
risk-adjusted returns. As more and more arbitrage capital enters
the market, the abnormal returns are reduced. Why can’t enough
capital be available to arbitrageurs so that the abnormal returns
become negligible? According to Mergerstat, the value of U.S. and
U.S. cross-border merger deals was $108 billion in 1990, $356 billion
in 1995, and $1,285 billion in 2000. Compared to this, the total mar-
ket capitalization of all stocks on U.S. exchanges at the end of 2000
was $11,750 billion. That is, mergers in 2000 were in excess of 10
percent of the entire market. With such a high volume of merger
activity, it is obvious that arbitrageurs are unable to command
enough capital to participate fully in more than a few deals. Per-
haps this is where the individual investors need to step in.
The Trading Process
Figures 9.1 and 9.2 depict a typical case. The speculation spread
narrows and eventually disappears in a successful merger.
It is not possible to use index futures or exchange-traded funds
for merger arbitrage because these financial instruments consist of
several hundred stocks, whereas the focus of merger arbitrage is on
single stocks. On the other hand, mutual funds, stocks, and options
can be used for realizing returns related to merger arbitrage. These
are discussed below. Among these, mutual funds are the easiest to
use and generate reasonable returns.
Beyond the Random Walk212
Bidder’s Offer and Target’s Actual Price
0 3 8 11 16 22 25 31 36 39 45 50 53 58 63 66 71
Days from Announcement
Arbitrage Spread for a Stock Merger
0 2 4 8 10 14 16 18 23 25 30 32 36 38 43 45 49 51 53 57 59 63 65 67 71
Days from Announcement
Figure 9.1 The figure shows the bidder’s offer price and the target’s actual price for
a typical stock merger. Information is plotted for Cardinal Health’s acquisition of
Bindley Western Industries in December 2000.
Figure 9.2 The figure shows the arbitrage spread or the difference between bidder’s
offer price and the target’s actual price for a typical stock merger. Information is plot-
ted for Cardinal Health’s acquisition of Bindley Western Industries in December 2000.
Merger Arbitrage 213
Options are not recommended for merger arbitrage because they
are too expensive. The value of an option can be divided into its
intrinsic value and its time value. The intrinsic value is the value an
investor realizes if the option is exercised immediately. The time
value of an option allows the investor to capture additional profits
if the stock price moves in the desired direction. The distinction
between these values is important, as the investor must pay for these
values when buying an option. Since merger arbitrageurs do not
attempt to time the market, the time value of the option is lost. Con-
sequently, merger arbitrageurs tend not to use stock options. Per-
haps for this reason the Merger Fund has only 5 percent of its deals
hedged using options—the remaining positions are taken by trad-
ing in stocks.
There are, however, three conditions under which options might
seem attractive. First, if there is significant risk of failure, then the
option can limit the loss. Second, an option may be used to lock in
gains already earned. For example, if the target in a cash offer has
appreciated from $20 to $25, then buying an at-the-money put op-
tion would lock in a profit of $5 (less the put premium). Third, in
the case of stock mergers, if it is not easy to short-sell, the investor
can buy a put option on the acquiring firm’s stock. Other than these
special cases, trading the underlying stock is a superior strategy.
USING MUTUAL FUNDS
Mutual funds that specialize in merger arbitrage are the simplest
vehicles for taking advantage of this mispricing. There are four
mutual funds that use most of their assets for merger arbitrage: the
Merger Fund, the Gabelli ABC Fund, the Arbitrage Fund, and the
Enterprise Mergers and Acquisitions Fund. Details relating to these
funds are in Table 9.5. The Merger Fund is the oldest and largest
fund. Between 1993 and 2002, it earned an average return of 9.7
percent annually with relatively low risk, compared with 11.5 per-
cent for the S&P 500 and 4.2 percent for one-month Treasury bills.
Further, the Merger Fund has earned superior returns, and better
than the risk-free interest rate in all years except 2001 and 2002. Ad-
justed for risk based on an estimated beta of 0.2, the Merger Fund
earned an annual abnormal return of 4.0 percent.5
Since the expense
ratio goes toward compensating the managers and for marketing
and administrative expenses, the true abnormal return of the Merger
Fund is 5.3 percent (4.0 percent + 1.3 percent).6
Table 9.5 Availability and Performance of Merger Arbitrage Funds
Gabelli Enterprise Lipper Risk-Free Research
Merger ABC Arbitrage M&A Merger S&P Rate Merger
Name of Fund Fund Fund Fund Fund Fund 500 (Annual) Arb Index
Ticker Symbol MERFX GABCX ARBFX EMAAX, LMFRX — — —
Date of January May September February August — — —
Inception 1989 1993 2000 2001 2001
Assets as of 1,000 158 84 57 NA — — —
(in $ millions)
Expense Ratio (%) 1.34 1.50 1.95 1.95 2.00 — — —
Beta of the fund 0.20 1.00 0.00 —
Total Return—2002 (%) –5.67 0.86 9.27 –3.79 NA* –22.1 1.75 –0.87
Total Return—2001 (%) 2.01 4.56 8.96 2.22 –0.70 –11.90 3.31 2.76
Total Return—2000 (%) 17.58 10.85 –8.49 5.67 18.02
Total Return—1999 (%) 17.39 9.00 21.68 4.52 14.34
Total Return—1998 (%) 5.35 11.14 29.53 4.60 7.23
Total Return—1997 (%) 11.65 12.75 33.73 4.96 16.44
Total Return—1996 (%) 9.95 7.90 23.28 4.98 16.61
Total Return—1995 (%) 14.15 11.07 37.82 5.32 17.86
Total Return—1994 (%) 7.13 4.53 1.35 3.91 8.88
Total Return—1993 (%) 17.69 9.90 2.85 20.24
Returns for EMAAX and LMRFX are for part of 2001.
*Ceased to exist in 2002.
Merger Arbitrage 215
Although the four funds invest primarily in merger arbitrage,
they may (and do) follow many related strategies. Thus, the returns
of these funds may be contaminated by other arbitrage activity. For
example, the Merger Fund routinely picks stocks that may be po-
tential targets or firms that were the subject of an unsuccessful take-
over attempt. The Gabelli ABC fund can engage in any kind of
arbitrage activity, though it concentrates on merger arbitrage. The
Enterprise Mergers and Acquisitions Fund also looks for firms that
are likely to be acquired.
To make sure the mutual funds are representative of pure merger
arbitrage, they are compared with the Hedge Fund Research’s
Merger Arbitrage Index until 2002 (available at www.hfr.com). The
returns are reported in the last column of Table 9.5. The average
return for the ten-year period until 2002 based on the HFR Merger
Arbitrage Index is 12.15 percent, which is comparable to the 11.06
percent (9.72 percent + 1.34 percent expense ratio) average return
earned by the Merger Fund. This suggests that the return earned by
the Merger Fund is representative of the actual returns earned by
Besides funds with direct interest in mergers, several other mu-
tual funds practice merger arbitrage. For example, Fred Alger Man-
agement (manager of Alger mutual funds) changed its holdings to
take advantage of the AOL–Time Warner merger that was an-
nounced in January 2000, as the numbers below illustrate. FredAlger
Management sold several million shares of AOL (acquirer) while at
the same time increasing its stake in Time Warner (target).7
that the reduction in AOL shares is larger than the increase in Time
Warner, in part due to the exchange ratio of 1.5 AOL shares for each
Time Warner share.
Holdings December 1999 March 2000 Change
Time Warner 51,900 1,584,000 +1,532,100
AOL 6,915,790 4,297,950 –2,617,840
The above discussion shows that it is possible to get reasonable re-
turns by using funds specializing in merger arbitrage. In addition to
mutual funds, numerous hedge funds also engage in this activity.
The remaining discussion focuses on the use of stocks in merger
arbitrage. The advantage of relying on stocks over mutual funds is
that the investor can hold potentially lucrative arbitrage positions
Beyond the Random Walk216
that a large arbitrageur is not interested in holding or is unable to
hold due to small target size, insufficient volume, or low price. Large
arbitrageurs may have resources to pick deals with a high probabil-
ity of success, but those deals generally have lower merger arbi-
trage spreads. To earn the returns documented in academic research,
the investor does not require superior information to select any par-
ticular deals, since the research includes all available deals in
computation of abnormal returns. Moreover, it may be possible to
earn better returns for selections based on factors that affect the ar-
The process for selecting deals and execution is as follows. Since
most deals are announced before the open or after the close, there is
enough time to obtain relevant information. If the time is insuffi-
cient, it is best to defer most trades toward the end of the day.
Factors for selecting deals are mentioned below.
1. Avoid deals with collars because they add uncertainty to an
arbitrage position and require more frequent monitoring than
pure cash or pure stock deals. Similarly, avoid deals that in-
clude warrants, units, preferred stock, and so on, because they
complicate arbitrage positions.
2. Avoid deals that are likely to be subject to antitrust scrutiny. To
identify such deals, look at the combined size of the target/
acquirer relative to the size of target’s market. Any merger that
will result in the merged firm accounting for more than 15–25
percent of the target’s industry is cause for concern. This is
especially true if no mergers have been attempted or if none
has been successful. For example, it is prudent to avoid merg-
ers in the airline industry, where several mergers have been
attempted but none successfully. The only exception to anti-
trust scrutiny is a failing-firm merger, where the firm would
go bankrupt unless it merges.
3. Choose deals where the target has a very large market capitali-
zation (more than $50 billion) because arbitrageurs may not
have the resources to fully participate in these deals.
4. Choose deals where the target has a low price (less than $10)
because arbitrageurs are unlikely to participate in these deals
due to high transactions costs.
Merger Arbitrage 217
5. Choose firms with low volume turnover (where volume of
shares traded per day is less than 0.5 percent of the total num-
ber of shares outstanding). Arbitrageurs are unlikely to par-
ticipate because they will not be able to hide their trades.
6. Choose deals with large arbitrage spreads carefully. Anything
more than 15 percent is suspect, although such deals also have
a high profit potential.
Recall that arbitrage positions for stock mergers are different than
those for cash mergers. Further, trading conditions on the NYSE are
slightly different from those on Nasdaq. Accordingly, the strategies
described below account for those differences.
Establishing Initial Position in Acquirers
1. Cash mergers. No action with respect to the acquirer is required
in cash deals, or deals where the value of the acquirer’s stock
is fixed although payment is in stock instead of cash. For ex-
ample, Johnson and Johnson’s bid of $109 in common stock
for each share of Cordis on October 19, 1995, is a cash deal
even though the payment to target shareholders is in Johnson
and Johnson stock. The reason it is treated as a cash deal is
because the dollar amount received by the target does not
change with a change in the acquirer’s stock price.
2. Stock mergers. For stock deals where the exchange ratio is fixed
(as in the AOL–Time Warner deal), the acquirer’s stock must be
sold short. The quantity to short-sell depends on the number of
shares promised by the acquirer for each share of the target.
3. NYSE acquirers for stock mergers. Prices on the NYSE are less
volatile than on Nasdaq and move more slowly because the
specialist must maintain an orderly and continuous market.
Since it is likely that the acquirer’s price will fall soon after the
market opens, place a market order before the market opens to
short-sell the acquiring firm’s stock. Note that execution of the
order may take time, as the broker tries to find shares to short-
sell. Cancel the order if it is not filled within the first fifteen to
twenty minutes after opening of the stock for trading (often
stocks with news open later than 9:30 A.M. on the NYSE). If the
acquirer’s stock cannot be short sold at the open, wait until
later in the day and try again.
Beyond the Random Walk218
4. Nasdaq acquirers for stock mergers. Due to high premarket trad-
ing in Nasdaq stocks and high price volatility immediately af-
ter the market opens, it is always prudent to wait until about
10 A.M. to place orders. In addition, it is best to specify a limit
price for short selling unless it is a very actively traded stock
with a daily volume of more than 2 percent of the number of
outstanding shares. In accordance with the strategy for stock
mergers, place an order to short-sell.
Establishing Initial Positions in Targets
1. Stock mergers. For stock deals, always short-sell the acquirer
before buying the target. Not only is it more difficult to short-
sell, but sometimes it is not possible at all. If you buy the target
before short selling, the profits could evaporate with a fall in
the target’s and acquirer’s stock prices while you try to short-
sell the acquiring firm’s stock.
2. Both stock and cash mergers. For NYSE targets, place a market
order at the open to buy the target. For Nasdaq targets, place a
limit order to buy the target around 10 A.M. Market orders are
appropriate only for actively traded Nasdaq stocks. The pri-
mary purpose of the limit is to remove any chances of a sur-
prisingly high price at which a market order is filled.
Unfavorable fills are common in illiquid stocks. The limit price
can be set at the ask price, just above or just below the ask
price, or just above the bid price.
3. Cash mergers. In the case of cash mergers, place a limit buy or-
der before the market opens, where the limit price is set 4–5
percent below the bid price. In this way, the speculation spread
will generate a sufficient return if the order is filled.
Closing Positions in Targets and Acquirers
The positions can be closed when the merger arbitrage spread has
narrowed considerably and there is no chance of another compet-
ing offer or when the merger is close to completion. There is no
need to wait until the merger is consummated.
Merger Arbitrage 219
Mergers During December 2000
Until now, all of the discussion has been based on prior research in
merger arbitrage. This section and the next section concentrate on
individual mergers, with a detailed discussion of one merger. Merg-
ers that were announced during December 2000 are listed in Table
9.6. The month of December 2000 is selected to allow sufficient time
for completion of mergers. The starting point for mergers is Thomson
Financial’s SDC Merger and Acquisitions database. To be included
in Table 9.6, each merger must meet the following criteria:
• The merger is first announced during December 2000.
• The target and the bidder are both publicly traded companies
in the United States. Foreign companies that trade on orga-
nized exchanges in the United States are also included. Bulle-
tin board stocks and stocks trading under $1 are excluded.8
• The market capitalization of the target prior to the bid is at
least $10 million.
• The mode of payment is either cash (90 percent or more) or
stock (90 percent or more) or a simple combination of the two.
• The entire target firm is being sold, not merely a few assets of
• The merger announcement is carried by news media such as
Business Wire, PR Newswire, Associated Press, and so on.
Table 9.6 has twenty mergers. None of the mergers is hostile, and
100 percent of the target is sought by the acquirer. Terms of offer
column gives details of the bid. “2.3 PEP” means that one share of
the target firm, Quaker Oats (OAT), will be exchanged for 2.3 shares
of the acquiring firm, PepsiCo. If a dollar amount is specified, then
the bid is a fixed-price cash bid for the target. The last merger has a
combination bid: $2 in cash plus 0.29 shares of the acquiring firm
for each share of the target. “First Trade Date After Bid” refers to the
first time an investor could have traded after the merger is an-
nounced. Thus, timing and date of the bid are very important. If the
bid is made before close of the market (4 P.M.) on a business day, then
that business day is the first trading day. If the bid is made after the
market closes, the first trading day is the next business day. The
speculation spread is the difference between the offer for the target
and the target’s closing price on the first trading day. In the case of
the PepsiCo–Quaker Oats merger, the merger was announced in
Table 9.6 Arbitrage for Mergers Announced in December 2000
Acquirer Size Prior Target
Acquirer Ticker to Offer Target Ticker
Name Symbol ($million) Name Symbol
1 PepsiCo PEP 61,150 Quaker Oats OAT
2 Cardinal Health CAH 27,770 Bindley Western BDY
3 BB&T BBT 13,250 Century South CSBI
4 Best Buy BBY 5,950 Musicland MLG
5 Nokia NOKS 250,000 Ramp Networks RAMP
6 United Community UCFC 250 Industrial Bancorp INBI
7 American Skiing SKI 43 MeriStar Hotels MMH
8 SouthTrust SOTR 5,950 Bay Bancshares BAYB
9 Swift Transportation SWFT 1,275 MS Carriers MSCA
10 Zions Bancorp ZION 5,060 El Dorado ELBI
11 CKF Bancorp CKFB 10 First Lancaster FLKY
12 FNB FBAN 446 Citizens Community CCBI
13 LVMH LVMHY 31,770 Donna Karan DK
14 Regions Financial RGBK 5,450 Morgan Keegan MOR
15 Berkshire Hathaway BRKA 104,000 Johns Manville JM
16 Microsoft MSFT 221,300 Great Plains GPSI
17 Northrop Grumman NOC 5,730 Litton Industries LIT
18 Hughes Electronics GMH 7,070 Telocity Delaware TLCT
19 Fulton Financial FULT 1,715 Drovers Bancshares DROV
20 GenesisIntermedia GENI 115 Fashionmall.com FASH
AVERAGE (EXCEPT #7, #20)b
#7 and #20 are excluded because they have very high speculation spreads, suggesting that
the mergers are likely to fail.
Beyond the Random Walk222
the morning on December 4, 2000. PepsiCo’s closing price that day
was $43.813, while Quaker Oats’ closing price was $91.06. However,
PepsiCo’s offer for Quaker Oats was $43.813 × 2.3 = $100.77. The dif-
ference between the offer and the actual price of the target is $9.71 or
10.7 percent. The merger was consummated 241 days later, and OAT
ceased to trade at that time. The raw return of 10.7 percent is annual-
ized to 16.6 percent based on the number of days to completion.
Table 9.6 shows several important points. About half the mergers
are pure stock mergers, and the remaining are pure cash mergers. A
collar is specified in only the PepsiCo–Quaker Oats merger. How-
ever, the collar did not get triggered because the price remained
within the primary range. The speculation spread is an indicator of
merger success. Typically, the spread is in single digits. However,
the spread is especially wide for mergers 7 and 20. In those cases,
the speculation spread is 39.9 percent and 68.9 percent. Such large
spreads suggest that the mergers are unlikely to succeed—in fact,
those are the only two bids that are eventually withdrawn. As dis-
cussed earlier and confirmed by the data in Table 9.6, it is prudent
to avoid mergers with large speculation spreads.
In Donna Karan’s merger, the speculation spread is zero. Very
small or negative spreads suggest the likelihood of higher bids.
Eventually DK was taken over at a price that was 26.2 percent above
the initial offer. While the possibility of higher bids increases the
returns to arbitrage, any such expectation must be tempered with
the probability of failure.
Overall, excluding the two bids with high speculation spreads,
the annualized return is 13.2 percent. This compares favorably with
the results in Table 9.1. The actual annualized return may be lower
for at least two reasons. First, transaction costs and bid-ask spreads
are not considered. Second, it may not be possible to easily short-
sell in all stock mergers.
The actual annualized return may be significantly higher in practice
for other reasons. First, December 2000 was a particularly bad month
for merger arbitrage. Due to deteriorating market conditions, the
chance of merger failure was much greater than normal. Moreover,
fewer mergers during that period meant that more arbitrage money
was available for merger arbitrage driving down the speculation
spreads. Second, it is possible and even desirable to close positions
prior to merger completion so that they generate higher annualized
returns due to the shorter holding period. Third, not all of the merg-
ers listed would make good candidates for merger arbitrage.
Merger Arbitrage 223
The following section evaluates several deals and provides a step-
by-step execution of merger arbitrage for one deal.
CHOOSING DEALS FOR MERGER ARBITRAGE
It is useful to consider each deal individually to determine whether it
would be desirable to take a position. The recommendations below
are based on the information available on the first trading day after an-
nouncement. The process of arriving at the recommendation does not
use any information not available at that time. Keep in mind that all
mergers are friendly or neutral, and there is no attempt by the target
management to reject the offer made by the acquiring firm.
Deal 1 (PEP-OAT) is a large merger in absolute terms. Since the
merging firms are in related industries, it is likely to raise some an-
titrust concerns. Though it may not affect the probability of success
or duration (see Table 9.5), the size of the target may still raise flags
that might delay the completion of the merger. On the other hand,
the speculation spread is large enough to make it attractive but not
too large to suggest a high probability of failure. Therefore, the rec-
ommendation is to accept the deal for merger arbitrage.
Deal 2 (CAH-BDY) is not large either in absolute terms or rela-
tive to the acquirer’s size. The merger is unlikely to encounter any
significant problems. The speculation spread of 4 percent is attrac-
tive. The recommendation is to accept the deal for merger arbitrage.
Deal 3 (BBT-CSBI) is also not large either in absolute terms or
relative to the acquirer’s size. The merger is unlikely to encounter
any significant problems. However, the speculation spread of 1.9
percent is small. Though BBT is actively traded, the daily volume of
CSBI averages about ten thousand shares, which means that the
bid-ask spread may be large. Indeed, the spread on CSBI prior to
announcement averaged 1–2 percent. Therefore, the recommenda-
tion is to reject the deal for merger arbitrage.
Deal 4 (BBY-MLG) is not large either in absolute terms or relative
to the acquirer’s size. The merger is unlikely to encounter any sig-
nificant problems. The speculation spread of 3.5 percent is attrac-
tive. Moreover, cash offers make it easier to trade by placing limit
orders at the time of buying and at the time of selling. The recom-
mendation is to accept the deal for merger arbitrage.
Deal 5 (NOK-RAMP) again is not large either in absolute terms
or relative to the acquirer’s size. The merger is unlikely to encoun-
ter any significant problems. However, the speculation spread of
Beyond the Random Walk224
1.4 percent is too small. Since it is a cash deal, it is possible to place
an order at a preselected limit price that would allow sufficient
speculation spread. For example, place an order to buy RAMP at
$5.60 (giving a profit of 3.5 percent). You would initiate merger ar-
bitrage only if your order gets filled at that price. In this particular
case, the order would have remained unfilled because the target’s
price never fell below $5.66. The recommendation is to accept the
deal for merger arbitrage only if the speculation spread is sufficient.
Deal 6 (UCFC-IBI) is not large in absolute terms but is large rela-
tive to the acquiring firm’s size. The large relative size may increase
the time for completion, but other than that no serious problems are
anticipated. The speculation spread is attractive, and it is a cash
bid. Therefore, the recommendation is to accept the deal for merger
Deal 7 (SKI-MMH) is not large in absolute terms but is large relative
to the acquiring firm’s size. The relative size and the extreme specula-
tion spread of 39.9 percent raise serious questions about success of the
deal. The deal should not be accepted for merger arbitrage.
Deal 8 (SOTR-BAYB) is similar to deal 4 and should be accepted.
Deal 9 (SWFT-MSCA) is large relative to the acquiring firm’s size,
and the time for completion is likely to be long. Coupled with a
small speculation spread for a stock deal, the deal should not be
accepted for merger arbitrage.
Deal 10 (ZION-ELBI) is similar to deal 2, though with a slightly
smaller speculation spread. The recommendation is to accept the
deal for merger arbitrage.
Deal 11 (CKFB-FLKY) is small in absolute terms but very large
relative to the acquirer’s size. The speculation spread is reasonable,
and it is a cash bid. However, the average trading volume in FLKY
is one hundred to two hundred shares a day with a wide bid-ask
spread. If the merger fails, it will become very costly to sell the
target’s shares. Therefore, the recommendation is to reject the deal
for merger arbitrage.
Deal 12 (FBAN-CCBI) is similar to deal 2 and quite attractive.
The only downside is that the target firm is not actively traded.
However, it seems very unlikely that the merger will fail. Thus, there
is no clear recommendation for this deal.
Deal 13 (LVMHY–DK) is in many ways similar to deal 5, except
that the speculation spread is zero. In fact, the speculation spread
occasionally became negative on the first day of trading suggesting
a strong possibility of higher bids for the target. Since revisions are
typically very profitable, the recommendation is to accept the deal
for merger arbitrage.
Merger Arbitrage 225
Deal 14 (RGBK-MOR) is similar to deal 4 and should be accepted.
Deal 15 (BRKA-JM) is similar to deal 5 with a similar recommen-
Deal 16 (MSFT-GPSI) is similar to deal 10 with a slightly smaller
speculation spread. The recommendation is to accept the deal for
Deal 17 (NOC-LIT) is large in absolute and relative terms. The
time period for completion is likely to be long. Since it is a cash
merger, the recommendation is to accept the deal only if a specula-
tion spread of at least 4 percent can be obtained.
Deal 18 (GMH-TLCT) is similar to deal 8 with a larger specula-
tion spread. The recommendation is to accept the deal for merger
Deal 19 (FULT-DROV) is similar to deal 2 and should be accepted.
Deal 20 (GENI-FASH) has an extremely high speculation spread
at 68.9 percent, which means that the bid will fail. Therefore, the
deal should not be accepted for merger arbitrage.
The average annualized return for the selected mergers is almost
16 percent. Coupled with low risk, this return far exceeds the nor-
mal market return.
EXECUTING A STOCK DEAL
A stock deal (deal 2: CAH-BDY) is selected for illustration because
stock deals are more difficult to execute than cash deals.
Step 1: Information about the deal. Cardinal Health’s (CAH) bid for
Bindley Western Industries (BDY) was announced by all major me-
dia sources around 6:30 A.M. on December 4, 2000. Most deals are
announced early in the morning, some in the evening, with very
few deals announced when the market is open. The CAH-BDY deal
seems to have a high probability of success. Four insiders holding
20 percent of the BDY stock have agreed to support the deal, and
the merger is expected to be completed in the first half of 2001. The
general consensus is that the deal will not be challenged by the Fed-
eral Trade Commission.
Step 2: Preopening stock prices. Obtain the preopening prices for the
merging companies at www.island.com and www.archipelago.com.
Preopening stock prices are easier to obtain for Nasdaq stocks than
for NYSE/AMEX stocks.
Step 3: Short-sell the acquirer. First, it is necessary to calculate the
number of shares to short-sell. If you buy five hundred shares of
BDY, you would sell 213.75 shares of CAH. However, 213.75 shares
is not a round lot. Therefore, you would short-sell 200 shares. It is
Beyond the Random Walk226
desirable to err on the lower side than on the higher side when short-
selling. Since CAH is an NYSE-traded stock, place a market order
to short-sell 200 shares. Assume that the order is filled at $94.563,
which is the closing price for December 4. Net receipt = $18,912.60
(price times quantity) minus $50 (one-half of bid-ask spread of $0.50)
minus $10 (broker’s fee) = $18,852.60.
Step 4: Buy the target. Immediately after the short sale order is
filled, place an order to buy five hundred shares of BDY at the mar-
ket, as BDY is a relatively actively traded NYSE stock. Assume that
the order is filled at $38.875. Net payment = –$19,437.50 (price times
quantity) minus $62.50 (one-half of bid-ask spread of $0.25) minus
$10 (broker’s fee) = –$19,510.
Step 5: Close the positions. The merger is actually consummated on
February 15, 2001. However, it is not necessary to wait until the last
day. On January 4, 2001, the closing price of $37.625 for BDY was
almost exactly equal to 0.4275 times the closing price of $88 for CAH,
giving a speculation spread near zero. Therefore, close positions on
January 4, 2001. Net payment from repurchase of CAH = –$17,600
(price times quantity) minus $50 (one-half of bid-ask spread of $0.50)
minus $10 (broker’s fee) = –$17,660. Net receipt from sale of BDY =
$18,812.50 (price times quantity) minus $62.50 (one-half of bid-ask
spread of $0.25) minus $10 (broker’s fee) = $18,740.
Step 6: Compute the return. Net profit = $18,852.60—$19,510—
$17,660 + $18,740 = $422.60 on an initial investment of $19,510 is 2.2
percent. Period of holding = thirty-one days. Annualized return =
about 26 percent.
The evidence presented in this chapter and the trading strategy rec-
ommendations rely on past data. Since future market conditions
and market patterns may change without notice, there is no cer-
tainty that merger arbitrage will continue to be profitable. Further-
more, the analysis is based on abnormal returns, not raw returns,
which means that if the market is falling, investors may lose money
even though abnormal returns are positive.
In addition, merger arbitrage can become particularly risky if the
deals are not carefully chosen. A broken deal can potentially wipe
away a significant portion of the profits earned from other deals.
Merger Arbitrage 227
• When a merger is announced, the stock price of the targeted
firm may be above or below the price promised by the bidder.
The difference between the actual price of the target and the
bidder’s offer is called speculation spread.
• A positive speculation spread (offer price > actual price) re-
flects the probability of failure and the duration between an-
nouncement and completion of the merger. A negative
speculation spread (offer price < actual price) means that higher
bids for the target, either from the same bidder or another bid-
der, are expected.
• The evidence indicates that the speculation spread is larger than
what it should be based on the duration and probability of fail-
ure. The purpose of merger arbitrage is to capture the excess
• Studies have documented abnormal annual returns between 4
percent and 34 percent for different samples and periods. These
returns are adjusted for risk, which is quite low for positions
in merger arbitrage.
• The arbitrage profit is affected by probability of success, time
from announcement to completion, and the degree of arbitrage
activity. If the speculation spread is high, the probability of
success is low. Although hostile bids are more likely to fail,
successful hostile bids generate larger profits. The probability
of success and the time to completion are negatively related.
Arbitrage activity depends on the arbitrageurs’ availability of
investment capital and their ability to hide trades from other
• Persistence of arbitrage profits can be attributed to transaction
costs, risk of arbitrage, and limited capacity. The most impor-
tant factor is limited capacity of arbitrageurs. Since capital must
find the highest available risk-adjusted returns, arbitrageurs
may only have restricted access to capital. Merger activity in
2000 was in excess of 10 percent of the entire market capitali-
zation—clearly, such a large amount of capital cannot be ear-
marked for merger arbitrage.
• Investors can use mutual funds to capture returns from merger
arbitrage or engage in merger arbitrage on their own using
Beyond the Random Walk228
stocks. The Merger Fund has generated an average annual ab-
normal return of 4.0 percent over the last decade. Hedge Fund
Research’s Merger Arbitrage Index suggests an annual abnor-
mal return of 6.4 percent without accounting for management
• An ad hoc sample of mergers from December 2000 generates
an annualized raw return of 13.2 percent. Since the risk pre-
mium during 2001 was negative, the abnormal return could be
• Not all announced deals are candidates for merger arbitrage.
If only the recommended deals are accepted, the annualized
raw return increases to more than 16 percent. Execution of one
stock deal is illustrated.
Merger arbitrage can generate continuous and sustainable abnor-
mal returns of 4–10 percent annually. Evidence relating to the prof-
itability of merger arbitrage is long-term and consistent.
Mutual funds specializing in merger arbitrage are a convenient
way to earn a reasonable yet low-risk return. Stocks can be used to
execute merger arbitrage transactions on an individual basis to pos-
sibly generate higher returns.
Mutual Funds Specializing in Merger Arbitrage
http://www.gabelli.com/funds/products/408.html: The site for Gabelli’s ABC
http://www.thearbfund.com: The site for the Arb Fund (ARBFX).
mergers_and_acquisitions.shtml: The site for Enterprise M&A Fund
Information Regarding Merger Deals and Statistics
http://www.thedeal.com: Has current news regarding deals. A table shows
speculation spreads of selected deals. A good source for active merger
arbitrageurs. Subscription is required.
http://www.dealanalytics.com: A good source for real-time news relating to
mergers, merging firms, arbitrage spreads, and so on.
http://www.mergerstat.com: Provides extensive statistics on mergers. Can also
provide databases of historical merger activity.
Merger Arbitrage 229
http://www.thomsonfinancial.com: Go to “Solutions for Investment Banks”
and then to “M&A.” Thomson Financial has numerous M&A-related
products. The data used in this chapter and many academic studies come
from SDC Platinum, which is owned by Thomson.
http://www.hfr.com: Hedge Fund Research’s Merger Arbitrage Index gives
performance of hedge funds primarily engaged in merger arbitrage.
http://www.nytimes.com: You can receive the daily DealBook by e-mail from
the New York Times by registering on their website.
firstname.lastname@example.org: Moreover.com will also
send you daily e-mails with merger news if you register by sending an e-
mail to the address given.
Stock Price Information
http://finance.yahoo.com: Contains historical and current stock price informa-
tion. You must make sure that the prices account for cash dividends and
http://www.archipelago.com and http://www.island.com: These are elec-
tronic communication networks (ECNs) or electronic marketplaces that
provide prices during trading hours and outside trading hours. However,
unlike Yahoo!, which provides aggregate information for all exchanges, the
ECNs provide prices only for trades executed through them.
References for Further Reading
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spectives on Mergers. Journal of Economic Perspectives 15(2), 103–20.
Baker, Malcolm and Serkan Savasoglu. 2002. Limited Arbitrage in Mergers and
Acquisitions. Journal of Financial Economics 64(1), 91–115.
Berkovitch, Elazar, and M. P. Narayanan. 1990. Competition and the Medium of
Exchange in Takeovers. Review of Financial Studies 3(2), 153–74.
Boesky, F. Ivan. 1985. Merger Mania—Arbitrage: Wall Street’s Best Kept Money-mak-
ing Secret (New York: Holt, Rinehart and Winston).
Bradley, Michael, Anand Desai, and E. Han Kim. 1983. The Rationale Behind In-
terfirm Tender Offers. Journal of Financial Economics 11(1), 183–206.
——— . 1988. Synergistic Gains from Corporate Acquisitions and Their Division
Between the Stockholders of Target and Acquiring Firms. Journal of Financial
Economics 21(1), 3–40.
Brown, Keith C., and Michael V. Raymond. 1986. Risk Arbitrage and the Predic-
tion of Successful Corporate Takeovers. Financial Management 15(3), 54–63.
Cornelli, Francesca, and David D. Li. 2002. Risk Arbitrage in Takeovers. Review of
Financial Studies 15(3), 837–68.
Dukes, William P., Cheryl J. Frohlich, and Christopher K. Ma. 1992. Risk Arbi-
trage in Tender Offers. Journal of Portfolio Management 18(4), 47–55.
Fishman, Michael J. 1989. Preemptive Bidding and the Role of the Medium of
Exchange in Acquisitions. Journal of Finance 44(1), 41–58.
Hansen, Robert G. 1987. Theory for the Choice of Exchange Medium in Mergers
and Acquisitions. Journal of Business 60(1), 75–96.
Hetherington, Norriss S. 1983. Taking the Risk out of Risk Arbitrage. Journal of
Portfolio Management 9(4), 24–25.
Beyond the Random Walk230
Jarrell, Gregg A., James A. Brickley, and Jeffrey M. Netter. 1988. The Market for
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Jindra, Jan, and Ralph A. Walkling. 2001. Speculation Spreads and the Market
Pricing of Proposed Acquisitions. Working paper, Department of Finance, Ohio
Karolyi, Andrew, and John Shannon. 1999. Where’s the Risk in Risk Arbitrage.
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——— . 2000. Hostility in Takeovers: In the Eyes of the Beholder? Journal of Fi-
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Product Price Effects. Journal of Business 69(2), 233–68.
Walkling, Ralph A. 1985. Predicting Tender Offer Success: A Logistic Analysis.
Journal of Financial and Quantitative Analysis 20(4), 461–78.
Welles, Chris. 1981. Inside the Arbitrage Game. Institutional Investor, August 1981,
1. The academic and practitioner literature calls this “risk arbitrage.” However,
the term “merger arbitrage” is more descriptive because “risk arbitrage” can
potentially refer to any arbitrage activity.
This chapter draws from a large number of published and unpublished
papers. Andrade, Mitchell, and Stafford (2001), Jensen and Ruback (1983),
and Jarrell, Brickley, and Netter (1988) review the evidence related to merg-
ers in different decades. Bradley, Desai, and Kim (1983, 1988), Kim and Singal
(1993), and Singal (1996) have discussed causes of mergers. The effect on
merger gains as determined by the mode of payment has been explored in
Hansen (1987), Fishman (1989), and Berkovitch and Narayanan (1990). Fi-
nally, these works on merger arbitrage have been extensively used in this
chapter: Baker and Savasoglu (2002), Brown and Raymond (1986), Cornelli
and Li (2002), Dukes, Frohlich, and Ma (1992), Hetherington (1983), Karolyi
and Shannon (1999), Larcker and Lys (1987), and especially Mitchell and
Pulvino (2001). Mark Mitchell is on leave from Harvard Business School and
runs a merger arbitrage fund along the lines discussed herein.
Merger Arbitrage 231
2. The only stories are Welles (1981) and Marcial (1983).
3. Appendix B has a primer on short selling. Short selling is significantly more
costly than buying shares due to a variety of institutional and legal restrictions.
4. Personal communication, Todd Pulvino, March 2002.
5. The abnormal return is calculated as the actual return minus the expected
return. Expected return is the risk-free rate plus market risk premium times
the beta. Thus, abnormal return = 9.7% – (4.2% + 0.2) × (11.5% – 4.2%)).
6. Note that costs of trading are already accounted for in the returns. The ex-
pense ratio typically consists of management fees, distribution and service
fees, and other administrative expenses. Thus, the expense ratio understates
the true returns from a particular strategy. Lipper Merger Fund, another
merger arbitrage fund, closed in 2002 due to lack of investor interest.
7. Institutional holdings in a stock are available at the end of each calendar
quarter, that is, as of December 31, March 31, etc. Hence, it is not possible to
report holdings exactly around the announcement of the merger.
8. Bulletin board stocks are not listed on NYSE, AMEX, or Nasdaq. Typically, a
broker will take your order and post it on a bulletin board announcing to
other traders that you are willing to buy a particular stock at a specific price.
If someone else is interested, that person will contact the broker and offer to
trade with you. Bulletin board stocks are difficult to trade and have wide
Beyond the Random Walk232
Financial economists have long maintained that all investors can im-
prove the quality of their portfolios by investing a significant part of
their portfolio in foreign securities. Including foreign assets reduces the
risk of the portfolio due to low correlations between foreign stocks and
domestic stocks without hurting return. However, individual investors
routinely underweight foreign assets, perhaps due to their ignorance.
While it is not possible to arbitrage home bias, investors should not
suffer due to a home bias in their own portfolios.
This chapter is about a long-term trading strategy.1
Too many in-
vestors fail to realize the importance of investing internationally
and consequently fail to obtain the best risk-return trade-off. This is
known as the home bias. The tendency of investors to be insufficiently
diversified is not limited U.S. investors, nor is it limited to foreign
stocks. Investors are routinely underdiversified and take on much
more risk than they are compensated for.
It is well known that investors are risk-averse. Such investors con-
sider both the risk and return of an investment and demand a higher
return for a riskier investment. It is no wonder that, in actual prac-
and the Home Bias
International Investing and the Home Bias 233
tice, higher-risk securities generate higher return. For example, the
expected return on Treasury securities (about 6 percent) is the low-
est because their risk is low. Corporate debt has the next higher
return (about 9 percent) because corporate debt is riskier than T-
bills. Stocks generate the highest return because stocks are the riski-
est.Among stocks, small stocks are generally considered riskier and
generate a higher return (18 percent) than large stocks (12 percent).
It is obvious that a risk-averse investor will choose the security
with the lowest risk among securities with the same return, and the
security with the maximum return among securities with the same
level of risk. Therefore, when possible, it is highly desirable to re-
duce a portfolio’s risk without affecting its return, or enhance the
return of a portfolio without increasing its risk.
DIVERSIFICATION OF RISK
It is possible to reduce the risk of a portfolio by adding stocks that
are not well correlated with the stocks in that portfolio. A simple
example is illustrative. Assume that you hold the stock of a com-
pany that sells beachwear. The annual return from the company’s
stock is 20 percent in sunny years with many sunny days but falls
to 0 percent in rainy years with few sunny days. Assume that the
probabilities of a sunny year and a rainy year are equal at 50 per-
cent. The average return is 10 percent, with a 50-percent chance of
20-percent return and a 50-percent chance of 0-percent return. Thus,
the beachwear company’s 10-percent return is risky.
How can you reduce the risk of your investment? Consider an-
other firm that rents videos. The video rental company is similar to
the beachwear company, except that its annual return is 20 percent
in a rainy year and 0 percent in a sunny year, with an average re-
turn of 10 percent. The video rental company’s 10 percent return is
also risky, just like the beachwear company’s return.
If you invest 50 percent each in video rental and beachwear, then
the average return is still 10 percent—50 percent of 10 percent from
video rental and 50 percent of 10 percent from beachwear. In a sunny
year you would earn 10 percent (50 percent of 20 percent from
beachwear + 50 percent of 0 percent from video rental). In a rainy
year you would also earn 10 percent (50 percent of 0 percent from
beachwear + 50 percent of 20 percent from video rental). Now, you
have no risk because you earn 10 percent in both sunny and rainy
years. Thus, by adding the video rental stock to the beachwear stock,
you have reduced your risk without affecting your return. The re-
sult is tabulated in Table 10.1.
Beyond the Random Walk234
You can see from the above table that the return is the same in all
cases—with a single stock or with both stocks. However, there is
risk with a single stock. You get either 20 percent or 0 percent. Once
you choose to invest in both stocks, the return becomes riskless be-
cause one of the two stocks does well and the other does poorly
regardless of the kind of weather.
The key in diversification of risk is correlation. Notice that the re-
turns from beachwear and video rental always go in the opposite
direction. If one of them does well, the other does not. Therefore,
adding stocks that do not behave like other stocks in your portfolio
is good and can reduce risk. The correlation is measured by what is
called a correlation coefficient. The correlation coefficient varies be-
tween –1 and +1. The two stocks in the above example have a corre-
lation of –1. Unfortunately, most stocks have a positive correlation,
and many of them have a correlation with the market portfolio that
is close to +1. The challenge in diversifying risk is to find stocks that
have a correlation of less than +1.
However, if you own only one stock, such as the stock of the com-
pany you work for, it is easy to find other stocks that are not well
correlated with that stock. Adding more stocks to that one stock will
certainly reduce risk. It is estimated that you must invest in thirty to
forty randomly picked stocks to get a reasonably diversified portfo-
lio. Did you know that a typical individual invests in less than ten
stocks? How many different stocks does your portfolio have?
Correlation and risk are important for all financial decisions. For
example, you protect your house and car against loss through in-
surance. Insurance has a negative correlation with your assets. In-
surance pays off when your assets are destroyed but pays nothing
if your assets are not destroyed. Moreover, the insurance actually
generates a negative return for you. You are willing to accept that
Table 10.1 Comparison of Returns with One and Two Stocks (in percent)
Sunny Rainy Average
Type Company % Invested Year Year Return
Single stock Beachwear 100 20 0 10
Single stock Video rental 100 0 20 10
Portfolio of Beachwear 50 20 0 10
two stocks Video rental 50 0 20 10
Total 100 10 10 10
International Investing and the Home Bias 235
negative return because insurance reduces your risk. Thus, it is not
unreasonable to accept negative returns if the addition of the in-
vestment generating the negative return reduces your overall risk
significantly. This important point underscores the trade-off between
risk and return: investors are happy to give up some return if the
reduction in risk is sufficient. Therefore, it is not always necessary
to ensure that the return is preserved.
Ageneral rule to evaluate whether a new asset should be included
in an existing portfolio is based on the risk-return trade-off rela-
= + × −
( ) ( )
n n p
n pf f
E R R E R R
where E(R) is the return from an asset, s is the standard deviation, r
is the correlation coefficient, and the subscripts n and p refer to the
new stock and existing portfolio. Rf
is the return on the risk-free asset.
If the new asset’s return is greater than the right-hand side in the
above equation, then the asset should be included in the existing port-
folio, otherwise not. That condition can be rewritten as below:
( ) ( )n pf f
E R R E R R
Before looking at the evidence, consider the potential benefits from
international investing and the source of those benefits.Assume that
the dollar return on U.S. stocks is 12 percent with a standard devia-
tion of 18 percent, and the dollar return on non-U.S. stocks is also 12
percent with a standard deviation of 18 percent. Since the U.S. mar-
kets and foreign markets are not well correlated, let the correlation
coefficient be 0.60. Putting the U.S. stocks and the non-U.S. stocks
in a 50-50 combination would generate a new world portfolio with
the following characteristics:
σ σ σ ρσ σ
−= + = × + × =
= + +
= × + × + × × × × × =
2 2 2 2
1 1 2 2 1 2 1 2
2 2 2 2
0.50 12% 0.50 12% 12%
0.50 0.18 0.50 0.18 2 0.50 0.50 0.60 0.18 0.18 0.16
w US non US
R w R w R
w w w w
Beyond the Random Walk236
The new world portfolio has a return of 12 percent and a risk of 16
percent. There is a reduction in risk from 18 percent to 16 percent
without a concurrent reduction in return. Thus, even when the for-
eign markets do not generate a higher return, the overall risk can
fall due to less than perfect positive correlation.
In this section, returns, risk, and correlations are presented along
with an optimal portfolio.
RETURNS FROM INTERNATIONAL INVESTING
For the purpose of investing, the world has been divided into three
main regions by the type of market: the United States, other devel-
oped markets, and emerging markets. All of the return data other
than data for the U.S. market have been obtained from the Morgan
Stanley Capital International indexes. The MSCI Europe, Australia,
and Far East (EAFE) consists of developed markets other than the
U.S. market. The emerging markets index (EMF) consists of emerg-
ing markets. There are two world indexes considered: the MSCI All
Countries (AC) index consists of all three regions and the MSCI All
Countries except the U.S. (AC-ex-U.S.) consists of MSCI EAFE and
MSCI EMF countries. All indexes are constructed by weighting the
constituents on the basis of the market capitalization of each coun-
try. You can see in Table 10.2 that the MSCI AC-ex-U.S. returns and
the MSCI EAFE returns are similar because the emerging markets
have a relatively small weight in the larger indexes.
Annual returns are reported for approximately fifteen years be-
ginning with 1988. The return of the last year (2002) is annualized
based on the first eight months of the year. The S&P 500’s return
varies from –27 percent to more than 37 percent, EAFE’s return is
between –20 percent and 35 percent, and the EMF return varies from
–30 percent to more than 75 percent. Overall, the S&P 500 return is
13.2 percent compared with 13.7 percent for emerging markets and
5.3 percent for the developed markets. Out of the fifteen annual
returns, emerging markets outperform other markets in eight years
and the U.S. markets are the best in six years, while the other devel-
oped markets are better than other regions only in 1994. The emerg-
ing market returns exceed 50 percent in four out of fifteen years.
If a different set of markets is considered, the results do not change.
Consider the developed markets alone: Japan, the United States,
Europe except the United Kingdom, the United Kingdom, and all
countries except the United States.Among these markets, the United
States outperformed the remaining markets only two times between
1987 and 2001. Just like with the beachwear and video rental com-
International Investing and the Home Bias 237
panies, it is smart to use a combination of countries and regions
than be restricted to the domestic market.
Though the results presented here are for the most recent fifteen-
year period, using earlier periods only strengthen these conclusions.
For example, if the 1971–88 period is considered, U.S. investors earned
an annual return of 9.9 percent. Compared to this, an investor who
held the EAFE portfolio would have earned 18.2 percent, nearly
double the return in the U.S. market. No data are available for the
emerging markets, as most of those markets were closed to foreign
investors at that time.An investor holding the world portfolio would
have earned 13.9 percent, 40 percent higher than the U.S. market.
What is obvious from Table 10.2 and other evidence cited is that
no single market is consistently the best-performing market. Amar-
ket may be good for one year, but a different market is likely to be
the best performer in another year.
Table 10.2 Annual Stock Returns by Region, 1988 to 2002 (in percent)
Australia, and Emerging All Countries All
the Far East Markets Except the U.S. Countries
Year S&P 500 (EAFE) (EMF) (AC-ex-U.S.) (AC)
1988 17.1 30.0 41.8 30.1 24.7
1989 32.5 12.3 71.2 13.0 18.7
1990 –1.6 –19.9 –6.8 –19.8 –14.5
1991 31.9 14.2 62.6 15.7 21.2
1992 7.9 –11.0 12.1 –10.1 –3.9
1993 10.3 34.8 76.5 36.9 25.6
1994 1.8 8.9 –5.5 7.9 5.7
1995 37.7 12.4 –4.1 10.4 19.9
1996 23.6 6.6 6.7 6.1 13.5
1997 34.9 3.3 –8.9 3.1 16.1
1998 31.4 22.4 –18.8 17.6 18.8
1999 22.0 28.3 70.5 31.4 33.8
2000 –7.9 –13.2 –29.7 –15.2 –13.1
2001 –10.2 –20.1 2.0 –18.2 –14.5
2002 –27.0 –15.4 –5.1 –14.5 –21.8
Average 13.6 6.2 17.6 6.3 8.7
The highest returns in a year are in bold. The returns include dividends and other distribu-
tions. All returns and classifications are based on Morgan Stanley Capital International in-
dexes, except that the S&P 500 returns are reported by Standard and Poor’s. Data are from
Global Financial Data and Barra. For 2002, only the return from January to August is used.
The return for 2002 reported in the table is annualized based on the first eight months. Author’s
Beyond the Random Walk238
RISK OF INTERNATIONAL INVESTING
The average return and the associated risk for each of the three re-
gions is in Table 10.3. The lowest risk, 14.3 percent, is for the U.S.
stock market whereas the highest risk, 23.9 percent, is for emerging
markets. The emerging markets also have the highest return of 17.6
percent compared to a return of 13.6 percent for the U.S. markets.
As a stand-alone market, the U.S. market is better than the EAFE
region but worse than emerging markets during the 1988–2002 pe-
riod. However, it will soon be apparent that even though the U.S.
market’s return is very good, it is still advantageous to invest in
The correlation matrix shows the correlations among different
markets. The correlation between the S&P 500 and the emerging
markets is only 0.42. With the developed markets, the S&P 500 has a
correlation coefficient of 0.58. Both of these correlations are quite
low. Similarly, the emerging markets and the developed markets
are not well correlated. On the other hand, the correlation between
the developed markets and the world without the United States is
1.00 because the contribution of emerging markets in the index for
all countries except the United States is quite small.
Correlations in different periods and among individual countries
provide a little more information about what can be expected in
terms of correlations in the future. If the period 1971–98 is consid-
Table 10.3 Return, Risk, and Correlations by Region, 1988 to 2002
Australia, and Emerging Except All
the Far East Markets the U.S. Countries
S&P 500 (EAFE) (EMF) (AC-ex-U.S.) (AC)
Annual Return 13.6% 6.2% 17.6% 6.3% 8.7%
Risk (standard 14.3% 17.0% 23.9% 16.9% 14.6%
S&P 500 1.00 0.58 0.42 0.60 0.70
Europe, Australia, 0.58 1.00 0.48 1.00 0.88
and the Far East
Emerging Markets 0.42 0.48 1.00 0.52 0.64
All Countries 0.60 1.00 0.52 1.00 0.88
except the US
All Countries 0.70 0.88 0.64 0.88 1.00
The data are as described in Table 10.2. The correlations are calculated based on monthly
returns. The standard deviation reported is annualized. Author’s calculations.
International Investing and the Home Bias 239
ered, the highest correlation between any two developed countries
is 0.70 (Canada and the United States). The lowest correlation is
0.25, between Italy and Australia. The 1980–92 period exhibits simi-
lar correlations: the highest correlation, 0.70, is between Canada and
the United States, and the lowest correlation, 0.24, is between Japan
and the United States. For the 1970–2000 period, the correlations
among developed countries vary from a low 0.25 to a high of 0.71.
For the 1971–88 period, the correlations among developed nations
vary between 0.14 and 0.70. The 1976–99 period shows correlations
in the range of 0.24 and 0.71 among developed nations and between
–0.05 and 0.48 among emerging markets and developed markets. If
individual years are considered, the correlations between U.S. and
developed markets vary between 0.3 and 0.8 over the last thirty
years with an average of 0.5. The correlations suggest a continuing
advantage from investing in foreign stocks.
CONSTRUCTING AN OPTIMAL PORTFOLIO
Since returns have been somewhat volatile over the years, the opti-
mal portfolio can vary with different periods. However, return vola-
tility underscores the need for controlling risk by diversifying
aggressively. Optimal portfolios recommended by prior research are
reported in Table 10.4. The recommendations have a common theme.
If you invest at least 30 percent in other developed markets, the
effect is a reduction in risk accompanied by an increase in returns.
This is a win-win situation.
None of the optimal portfolios include exposure to emerging mar-
kets because emerging markets are small, they are considered to be
very risky, and the correlations can increase significantly. However,
the key is that the correlation between emerging markets and the
U.S. market is still much less than the correlation between the U.S.
market and other developed markets, and the return can be higher.
Therefore, it is worthwhile to invest a nontrivial amount in emerging
markets. The following allocation among global stock markets can
be considered reasonable to obtain the benefits of diversification.
U.S. stocks 60%
Other developed markets 30%
Emerging markets 10%
AN ESTIMATE OF THE HOME BIAS
The evidence of optimal investment suggests significant investment
in foreign stocks. How do investors compare with the recommended
Table 10.4 Optimal Portfolios for Different Periods
Period of U.S. Portfolio (%) Allocation (%) Portfolio (%)
Analysis Return Risk U.S. EAFE Return Risk Comments
1970–2000 12.70 15.30 19.60 18.60 Much higher return and risk
1970–2000 12.90 15.40 70 30 13.00 14.00 Same return, lower risk
1971–1998 13.40 15.30 13.50 14.30 Same return, lower risk
1980–1992 17.20 15.80 41 59 20.00 14.50 Higher return, lower risk
1971–1988 9.90 16.20 13.90 14.50 Higher return, lower risk
1971–1988 9.90 16.20 100 18.20 17.50 Much higher return, higher risk
International Investing and the Home Bias 241
global allocations? The difference between the recommended allo-
cation in foreign stocks and the actual allocation in foreign stocks is
referred to as the home bias. Though the actual investment in for-
eign stocks has increased severalfold, from 1 percent in 1980 to 7
percent in 2000, U.S. investors remain woefully underdiversified.
Compared with the recommended allocation in foreign stocks of 40
percent, the 7 percent allocation means that the home bias results in
33 percent excessive investment in domestic stocks.
There is another way of looking at the home bias. Some observ-
ers believe that investors should hold the world market portfolio
passively, just as they do for domestic securities, where investment
in a market index is considered appropriate. This means that if the
capitalization of the U.S. markets is 47 percent of the worldwide
total, then 47 percent should be invested in U.S. stocks and the re-
mainder in foreign stocks. Using this measure of home bias, it is
also possible to estimate the home bias for investors in other coun-
tries. Estimates of the home bias are reported in Table 10.5. Ameri-
can investors have the lowest home bias, perhaps because of the
size of the market. Swedes and the Dutch invest the most in foreign
equities among the developed countries. Thus, the incidence of home
bias is not restricted to American investors alone but is a world-
Table 10.5 Estimates of Home Bias (in percent)
Capitalization in Domestic
Country as % of World Stocks Home Bias
Australia 1–2 88 >85
Canada 2–3 88 >85
France 5 83 >75
Germany 5 80 >70
Italy 2–3 93 >90
Japan 13 91 >75
Netherlands 2 75 >70
Spain 1–2 95 >90
Sweden 2 72 >65
UK 8–9 78 >65
US 47 90 >40
Adapted from Jeske (2001).
Beyond the Random Walk242
HOME BIAS ALSO EXISTS FOR DOMESTIC STOCKS
The term “home bias” is normally associated only with foreign
stocks. However, “home” can be much closer to home. Home bias
also exists for domestic stocks in addition to foreign stocks. Evi-
dence shows that investors tend to invest in companies that they
are aware of. For example, a disproportionately large number of
investors in phone companies come from the states that the compa-
nies serve, though from an investment perspective the location of
the company should be inconsequential. Even institutional investors,
such as mutual funds, tend to invest in companies that are located
close to their own corporate offices. Perhaps investors heed the ad-
vice of celebrities like Peter Lynch, who suggest that people should
invest only in the companies they know well.
HOME BIAS IS WORSE THAN YOU THINK
Whenever an individual’s portfolio is considered, all of the possible
assets must be considered, financial and nonfinancial. However, the
evidence presented above is based on equity markets only. In addi-
tion to marketable equity there is private equity in companies not
publicly traded. There are fixed-income assets such as government
bonds and corporate bonds. There is real estate. And, finally, even
human capital is an asset.
Among all nonmarketable assets, human capital is probably the
most important. Since human capital is highly correlated with an
individual’s job and eventually with the domestic economy, a large
proportion of an individual’s capital is invested in the domestic
market. On the other hand, human capital is very weakly corre-
lated with foreign markets. According to one estimate, once human
capital is taken into account, a typical investor should not be in-
vested in the domestic market at all. All marketable assets should
be invested in foreign markets alone. Moreover, when you consider
other assets such as bonds, real estate, and private equity, the home
bias becomes much worse than that documented above.
BONDS CAN HELP WITH DIVERSIFICATION
If the correlation among different assets is important for minimiz-
ing risk, then bonds should play a critical role. Some correlation
coefficients are illustrative. Based on the 1971–98 period, the corre-
lation between U.S. stocks and Swiss bonds is –0.03, 0.21 between
International Investing and the Home Bias 243
U.S. bonds and Italian bonds, and 0.20 between Canadian bonds and
French bonds. The correlation between U.S. stocks and U.S. bonds is
also low: only 0.45 based on a fifteen-year period ending in 1985.
Therefore, an ideal portfolio should consist of U.S. stocks, for-
eign stocks, U.S. bonds, and foreign bonds. Due to ease of availabil-
ity of data and analysis, the remainder of the chapter continues to
focus on marketable equity assets only.
Concerns and Limitations
There are a variety of concerns with international investing and limi-
tations of the analysis cited in previous sections. These limitations
are discussed below and may weaken the case for international in-
INCREASING AND VARYING CORRELATIONS
The key benefit from international investing arises because of low
correlations between the domestic market and foreign markets.
There are two criticisms of historical correlations. First, the correla-
tions may be increasing due to greater global integration as evi-
denced by larger capital and trade flows. Moreover, as more and
more emerging markets liberalize capital flows, the correlations will
increase. If the correlations are increasing, the above analysis based
on prior data overestimates the benefit from international invest-
ing. Reconsider the example in the preamble of “Evidence,” above.
With a correlation of 0.60, the new portfolio’s risk fell from 18 per-
cent to 16 percent. However, if the correlation is 0.70 instead of 0.60,
then the new portfolio’s risk falls less, from 18 percent to 16.6 per-
cent. If the correlation is 0.8, then the risk is 17.1 percent.
You can see that the gains from international investing can quickly
erode with an increase in correlations.
The second criticism stems from evidence that suggests that cor-
relations increase in times of booms and crises. Since risk diversifi-
cation is most useful and critical when markets are in a decline or in
turbulent markets, increasing correlations at those moments make
international investing less attractive. For example, all markets fell
together during the 1974 oil price shock, the 1987 stock market crash,
the 1991 Gulf crisis, and the 1997 East Asian currency crisis. Clearly,
the higher correlation in times of crisis is not desirable.
Beyond the Random Walk244
From Table 10.2, the average correlation is 0.58 for the developed
markets and 0.42 for the emerging markets. The different periods
considered in “Risk of International Investing” suggest that corre-
lations vary between 0.20 and 0.70 for pairs of developed countries
and that the range has not varied much over time. In any case, how
high can the correlations go? The United States and Canada are prob-
ably as similar as two countries can be and trade a lot. However, the
correlation has hovered around 0.70. The same thing is true of Swit-
zerland and Germany. Thus, there seems to be an upper bound to
how correlated U.S. markets and foreign markets can become.
Why is there an upper bound? The answer is in the two sources
of diversification that cause the countries to be less than perfectly
correlated. The first source is based on differences in the political
and economic environment of different countries. The second source
of low correlation is differences in the industrial makeup of coun-
tries. The argument goes as follows: the political outlook and eco-
nomic structure of a country is important because a centrally planned
economy will behave quite differently than a market-driven economy.
Changes in the political climate do not affect more than one country
or region. For instance, political turmoil in Indonesia may affect
Singapore and Malaysia but is unlikely to affect the U.S. stock mar-
ket. The political relationship between North Korea and South Korea
is unlikely to have an effect on European markets. Similarly, national
stock markets may continue to remain poorly correlated if those mar-
kets consist of different industries. For example, a country that spe-
cializes in textiles cannot be highly correlated with the U.S. stock
market, which consists of high-tech and service-oriented industries.
Moreover, while globalization can increase correlations among
countries due to integration, globalization can also lead to lower
correlations. With greater trade and globalization, countries tend to
specialize in industries depending on comparative advantage, their
natural resources, labor skill, wages, and so on. As the developed
countries move more toward services and concentrate on innova-
tions, they will import more of other products. Therefore, global-
ization makes the countries more different due to specialization.
This specialization in industries suggests that it is unlikely that the
industrial base of countries will converge, and hence the stock mar-
kets are unlikely to become highly correlated.
The jury is still out on the relative importance of the two sources
of diversification. Are differences in political and economic envi-
ronment more important than differences in the industrial struc-
International Investing and the Home Bias 245
ture of countries? Whatever the cause, it is easy to see that countries
will remain less than well correlated for a long time. From a histori-
cal perspective, global trade as a percentage of GDP was at a sig-
nificantly higher level in the early 1900s than today, but the
correlations among countries were not high. Individual country cor-
relations have bounced around and increased a little, but the EAFE-
U.S. correlations have remained between 0.50 and 0.60.
On the other hand, the correlations between emerging markets
and the U.S. market are likely to increase as the emerging markets
become more open to foreign capital flows. However, these correla-
tions do not increase continually. Take the 1984–93 period. The cor-
relation between the U.S. and a composite of emerging markets was
0.34 for 1984–88, but it fell to 0.20 between 1988 and 1990 and then
to 0.19 for 1991–93. Though there is an increase in correlations, they
will probably stagnate around 0.40 and 0.50. A low level of correla-
tion with emerging markets is appropriate due to large differences
in economic conditions and prosperity.
The second concern relates to higher correlations in times of cri-
sis. There are two responses. First, other studies question the reli-
ability of this finding and state that correlations only seem to be
higher and in fact are actually the same. Second, the correlations
mentioned above and used in calculations include both highly vola-
tile and normal times. Since any equity investment, including inter-
national equity investment, ought to be long-term, very short-term
correlations are not relevant.
COSTS AND TAXES
The cost of investing internationally is significantly higher than in-
vesting domestically because of many factors. First, gathering in-
formation about foreign stocks is more expensive. Foreign companies
reveal much less information about their operations than their
American counterparts because they do not have the same kind of
disclosure requirements. Moreover, the information that is avail-
able in the public domain is more difficult to obtain and more ex-
pensive. Investors must subscribe to foreign database subscription
services, fax services, and foreign newspapers and pay for expe-
dited delivery to obtain the information in a timely manner. And
differences in accounting practices mean that financial statements
are not easily comparable. These difficulties make research required
to value foreign company more expensive and more uncertain.
Beyond the Random Walk246
The second cost factor relates to the cost of trading. Trading costs
consist of exchange commissions, brokerage commissions, transac-
tion taxes, and market impact costs. Exchange costs must be incurred
for converting dollars into another currency. Depending on the cur-
rency, these costs range between 0.05 percent and 0.1 percent for the
more actively traded currencies and up to 0.25 percent for other
currencies. In addition, foreign brokers charge higher commissions
than U.S. brokers. Compared to a fee of 0.1 percent for large trans-
actions in the United States, foreign brokerage commissions can run
from 0.1 percent to more than 1.0 percent in other countries, includ-
ing developed markets. Almost all governments impose taxes on
stock trades. In the United States there is an SEC fee that is cur-
rently 0.00301 percent on all stock sales. Other governments may
and do charge much higher fees, as much as 0.5 percent of the sale
amount. Some countries charge fees on both buys and sells. Besides
the fees and commissions, there is a market impact cost that must
be borne by the investor. Whenever large trades are made, there is
an impact on the price. If a large buy order is placed, the price in-
creases to induce more market participants to part with their stock.
Similarly, when a large sell order is placed, the price falls so that the
stock becomes attractive to reluctant buyers. This impact on price
occurs in all markets. However, the price impact of a trade is likely
to be larger in foreign markets because they tend to be smaller and
less liquid than U.S. markets. The high trading costs reduce the re-
turns available from international investing.
Another form of tax is the withholding tax on dividends. This tax
is usually about 15 percent and withheld by the foreign govern-
ment. The investor must claim a set-off against other taxes. The with-
holding tax creates two problems. First, the extra hassle of paying
taxes and then reclaiming those taxes with a time lag is a cost in-
curred by investors in foreign securities. Second, tax-exempt inves-
tors such as pension plans completely lose the withholding tax
because they are not liable for payment of any income taxes.
All of the above costs due to information, trading, and taxes were
ignored in prior analyses. The firm of Elkins and McSherry reports
that costs directly related to trading vary considerably among the
forty-five emerging and developed markets. It finds the highest
trading costs among emerging countries for Venezuela (2 percent),
highest among developed markets for Ireland (0.90 percent), and
the lowest among developed markets for Japan at 0.22 percent.
The trading costs in American and German markets are about 0.29
International Investing and the Home Bias 247
Information costs, trading costs, and taxes can indeed reduce the
net return earned from foreign investments. However, the costs are
still smaller than the gains from international investing. In addi-
tion, for most individual investors, American depository receipts
(ADRs, discussed below) provide an easy and inexpensive way to
trade where the costs of trading foreign stocks are equivalent to
those for trading domestic stocks.
Holding foreign securities denominated in foreign currencies en-
tails currency risk, as dollars must first be converted into foreign
currencies and the foreign currencies converted back into dollars at
the future rate. As the future rate is unknown, investing in foreign
markets suffers from an additional risk due to currency fluctuations.
Yes, there is currency risk due to currency conversions and uncer-
tainty with regard to future exchange rates. However, as all of the
returns reported in the earlier tables are in dollar terms, those re-
turns already incorporate associated currency risk. Thus currency
risk is important in foreign investments but has already been ac-
counted for. Currency risk can also be hedged if desired (see “Cur-
POLITICAL AND ECONOMIC RISK
Investors are also concerned about big changes in the economic con-
ditions due to a change in the political orientation of the government.
While this is of most concern in emerging markets, even the devel-
oped markets are not immune to a dramatic change in the environ-
ment. Obviously, large changes are risky for equity markets. In
addition, foreign investors are also concerned about currency regula-
tions that may hinder repatriation of capital/income. For example,
Malaysia did not permit repatriation of capital for one year follow-
ing the 1997 EastAsian currency crisis. Other countries routinely make
it difficult for investors to transfer funds out of the host country.
Beyond the Random Walk248
This is a valid concern. However, there are numerous stock mar-
kets. It is easy to exclude countries that have an unstable political
history or have restricted capital flows in the last decade. An inves-
tor can pick many developed markets and emerging markets where
the political risk is relatively low. See “Internet References” for
websites providing this information.
LIQUIDITY RISK AND MARKET INEFFICIENCY
The size of the markets can work against foreign investors in two
ways. First, some securities and some countries may be illiquid. In
such markets, any reasonably sized trades are sufficient to move
the price. The price rises when one wants to buy and falls upon a
sale. This is particularly painful because most foreign investors end
up selling and buying around the same time.
The second concern with market size is inefficiency. Emerging
markets are known to be inefficient, and prices can take several days
to fully reflect new information. As a passive investor, you can lose
money to more sophisticated investors who trade on the basis of
Liquidity risk exists in all markets, including the U.S. market, where
small stocks are very illiquid. The challenge is for the investor to se-
lect markets and stocks that are likely to experience a smaller liquid-
ity shock than other countries and stocks. So it would be smart for
investors to trade only large, liquid stocks in large, liquid markets.
Market inefficiency can work both ways. It certainly worsens the
returns for unsophisticated investors, but smart investors can take
advantage of the inefficiencies, thereby forcing the market to be-
come more efficient. In any case, passive investors can choose mar-
kets that are relatively less inefficient.
RISKINESS OF FOREIGN MARKETS
Foreign markets are very risky, much riskier than the U.S. markets.
Risk-averse investors are unwilling to accept a higher level of risk.
International Investing and the Home Bias 249
Foreign markets, especially emerging markets, are indeed riskier
than U.S. markets. However, due to the low correlation between
foreign markets and U.S. markets, a portfolio that includes stocks
from both markets need not be as risky. The diversification of risk
has been illustrated in Tables 10.3 and 10.4. As a matter of fact, hold-
ing U.S. stocks only is riskier than holding a world portfolio
weighted by the market capitalization of each country.
The home bias is nothing new and has persisted for decades. Though
the investment in foreign equities has increased from 1 percent to 7
percent over the last two decades, it falls short of the level of opti-
mal foreign investment.
Unlike the mispricings discussed in earlier chapters, it is not pos-
sible for arbitrageurs or anyone else to form short-term trading strat-
egies. Over the long term, however, investors who hold foreign
stocks will outperform portfolios that are restricted to domestic
The only reason that can explain the persistence of the home bias
is the ignorance of a typical investor. A comparison of investment in
foreign stocks by individual and institutional investors is revealing.
According to Fidelity and Pensions and Investments, only 3 percent of
the assets held by individual investors are invested in foreign equity,
compared with 13 percent for professionally managed pension funds.
The two hundred largest corporate pension plans had an allocation
of 16 percent to foreign stocks. On the other hand, mutual funds have
only 3.5 percent invested in international stocks. The foreign alloca-
tion of mutual funds mirrors the individual investor allocation be-
cause individual investors can pick and choose mutual funds and
exclude international mutual funds if they don’t want to invest inter-
nationally. The pension funds can determine the allocation on the
basis of portfolio theory, as discussed in this chapter.
Where and How to Invest Internationally
Buying foreign stocks is cumbersome for an individual investor
because it requires currency conversion, opening an account with a
foreign broker, taking custody of a foreign company’s shares, and
Beyond the Random Walk250
all the associated transactions. Many domestic brokers now offer
trading in foreign stocks, but it is still a lot more difficult to buy and
sell foreign stocks than it is to trade domestic stocks.
There are, however, alternatives available that do not require di-
rect trading on foreign stock exchanges. These are American de-
pository receipts (ADRs), mutual funds, exchange-traded funds, and
multinational companies. Details are provided below.
AMERICAN DEPOSITORY RECEIPTS (ADRS)
ADRs are negotiable registered certificates that stand in for the un-
derlying stock of foreign companies. A U.S. bank (called a custodian
bank) holds shares of foreign companies and issues receipts (ADRs)
against those shares. There could be one ADR for several shares or
several ADRs for one share of stock—the custodian bank picks a ra-
tio that puts the ADR in a tradable range of $50–100. For example,
each share of British Petroleum is subdivided into six ADRs and each
share of BritishAirways is equal to tenADRs, while two Honda shares
make one ADR but one Sony share is equal to one ADR.
The Bank of New York holds the largest number of shares as a
custodian, though J. P. Morgan created the first ADR in 1927 for
investing in the British retailer Selfridge’s. The certificates are quoted
in U.S. dollars and dividends are paid in U.S. dollars. ADRs are
traded on the major U.S. stock exchanges or over the counter. ADRs
are issued in two basic versions: sponsored and unsponsored. The
most popular version today is sponsored, and for these, the cre-
ation of the ADR is initiated and supported by the company. As of
2002 there were 1,450 ADRs, including 200 unsponsored ADRs.
There are four kinds of sponsored ADRs.
• Level I ADRs trade on the pink sheets (OTC bulletin board), are
exempt from the SEC reporting requirements, but cannot be used
for raising capital, or be listed on organized stock exchanges in
the United States. More than eight hundredADRs, such as Roche,
Nestlé, and Volkswagen belong to this category.
• Level II ADRs are listed and trade on U.S. exchanges—NYSE,
AMEX, Nasdaq—but cannot be used for raising new equity
capital. Financial statements must be partially reconciled with
generally accepted accounting principles (GAAP).
• Level III ADRs can raise new capital from American investors
and are listed on U.S. exchanges. These ADRs are just like do-
mestic stocks and require full compliance with GAAP and SEC
International Investing and the Home Bias 251
• Rule 144A ADRs: Under Rule 144A, a company can raise new
capital but only from qualified institutional buyers (QIB) and
a limited number (thirty-five) of noninstitutional buyers. This
provides another way of raising new capital but without com-
pliance with GAAP/SEC regulations.
The biggest advantage of an ADR is the ease with which it can be
traded. To buy Nokia, you would call your broker and tell him/her
to buy Nokia just as you would tell him/her to buy IBM. You get all
of the benefits of foreign ownership but are able to minimize the
costs associated with foreign trading. With level II and III ADRs,
you get more information and are better protected against fraud
Unfortunately, ADRs may not represent all industries and coun-
tries. Typically, ADRs are issued for companies that sell consumer
goods because those companies will be known to American inves-
tors and will attract investment capital. ADRs have no voting rights
may be an issue for some ADRs because the U.S. market shares typi-
cally represent less than 10 percent of all outstanding shares.
INTERNATIONAL MUTUAL FUNDS
Nearly all of the mutual fund families offer multiple funds that are
geared toward international investing. The different kinds of funds
can be categorized into index funds, international funds, regional
funds, country funds, emerging market funds, and global funds.
International mutual funds have higher expense ratios than domestic
mutual funds to cover higher trading costs and higher management
fees. The funds also tend to have redemption fees to control fre-
quent trading. Examples of funds offered by major mutual fund
companies are given below.
• Index funds. These include Fidelity Spartan International Index
Fund, Vanguard Developed Markets Stock Index, Vanguard
Emerging Markets Stock Index, and Price International Equity
• International funds. These funds do not invest in the domestic
market. Funds include Fidelity International Growth, T. Rowe
Price International, Fidelity Overseas, Vanguard International
Growth, Fidelity Diversified International, and so on.
• Global funds. These funds invest in all countries, including the
domestic market, and include Templeton World, GT Global
Beyond the Random Walk252
Worldwide, Dreyfus Global, Vanguard Global Equity, Price
Global Stock, and so on.
• Regional funds. Examples include Fidelity Europe Capital Ap-
preciation, Fidelity Nordic, Vanguard European Stock Index,
and T. Rowe Price European Stock.
• Country funds. Examples include Fidelity Canada and Fidelity
Japan Smaller Companies.
• Emerging market funds. Examples include Fidelity Emerging
Markets Fund, Fidelity Latin America, and T. Rowe Price
Emerging Markets Stock.
EXCHANGE-TRADED FUNDS AND CLOSED-END FUNDS
Both exchange-traded funds (ETFs) and closed-end funds trade on
organized exchanges, just like stocks. Unlike mutual funds, which
are priced at the end of the day, ETFs and closed-end funds can be
traded at any time during trading hours with no restrictions or re-
Closed-end funds were started several decades ago, when many
markets were closed to foreign investment. For example, Scudder
Investments was permitted to invest $100 million in Korea in April
1984 with the condition that the money could not be taken out of
Korea, nor more money brought in. As a result, the fund cannot
redeem shares nor issue more shares. In other words, it is a closed-
end fund. Any shareholders of the Korea Fund can sell shares only
on an exchange, like the NYSE. Similarly, new investors must buy
shares on the NYSE. One problem with the closed-end funds is that
they usually trade at a discount (sometimes at a premium) to the
underlying value of the securities held. The reasons for the discount/
premium are not well understood, so many investors tend to avoid
Exchange-traded funds track an index by holding the stocks in
that index. There are iShares for twenty countries that track the MSCI
(Morgan Stanley Capital International) country indexes, and three
regional indexes. The regional ETFs are for the Pacific except Japan,
EAFE, and the EMU. The EMU fund is for countries that participate
in the euro. In addition to the ETFs that track MSCI indexes, there
are four ETFs that track S&P international indexes: Latin America,
Topix (Japan), Europe, and Canada. The ETFs track the underlying
indexes quite well, with a correlation of about 0.97. At the same
time, the correlation of ETFs with the S&P 500 is low. Thus, ETFs
are effective in diversifying the risk of a domestic portfolio.
International Investing and the Home Bias 253
The expense ratio of the ETFs is less than 1 percent, which is less
than the expense ratio for mutual funds. However, there are other
costs of trading ETFs such as brokerage commissions and the bid-
ask spread. Unlike the popular ETFs such as SPY (for the S&P 500)
and QQQ (for the Nasdaq 100), international ETFs may not be ac-
tively traded. Investors may not want to trade ETFs if the daily av-
erage volume is less than a hundred thousand shares.
The last possible avenue for obtaining international exposure is
multinational companies with large overseas operations. As these
companies operate globally, their stocks should provide the diver-
sification expected from foreign stocks. However, research suggests
that multinational companies are not good substitutes for foreign
The failure of multinational companies to diversify risk should
not come as a surprise once you consider the correlation between
the S&P 500 and companies with large overseas operations.
Company S&P 500
General Electric 0.97
Exxon Mobil 0.96
Chevron Texaco 0.94
AI Group 0.93
A correlation of more than 0.90 means that there is unlikely to be
a significant improvement in risk by the addition of or overweighting
of these companies in a domestic portfolio.
EFFECTIVENESS OF THESE INSTRUMENTS IN DIVERSIFICATION
Though the ADRs and ETFs do not span the entire spectrum of for-
eign markets, they help in substantially diversifying risk. The addi-
tion of international mutual funds to ADRs and ETFs almost fully
captures the benefits of international investing, eliminating the need
for an individual investor to invest overseas directly.
Beyond the Random Walk254
One issue that has elicited different responses is the role of currency
risk in overall risk and return. Currency risk has been accounted for
in all of the evidence presented. So the existence of currency risk
will not reduce the benefits of investing in foreign markets. Rather,
the question is whether managing currency risk will improve the
gains from international investing.
While the reduction of any kind of risk is good, there are two
issues that must be considered with regard to currency risk. First,
the correlation between currency risk and stock market risk is close
to zero. That means that currency changes and stock returns are
independent of one another. Though both currency risk and stock
market risk contribute to the total risk of a portfolio of foreign stocks,
the contribution of currency risk to the total risk is not very large
because of the zero correlation. On average, currency risk contrib-
utes less than 20 percent of the total risk.
The second issue is the cost of hedging currency risk. To com-
pletely eliminate currency risk, a dynamic hedging strategy is re-
quired, which can be very expensive. Even incomplete hedging can
be costly due to the time required and the expense of putting the
hedge in place. Consider an investment in the EAFE index. For a
given level of risk, the hedged portfolio has a return that is at most
0.5 percent higher than an unhedged portfolio. If the cost of hedg-
ing is less than that, hedging is worthwhile; otherwise it is not.
The case for hedging an investment in emerging markets is even
weaker because the correlation between currency risk and stock
market risk is very often negative. In such cases, hedging currency
risk will increase the total risk instead of reducing total risk.
The performance of foreign portfolios including international
mutual funds can depend a great deal on whether the funds hedge
against currency risk or not.Acomparison of the MSCI EAFE hedged
and unhedged indexes is telling. The hedged MSCI EAFE index lost
only 4.4 percent in 2000 compared with the unhedged index that
lost 14.2 percent in the same period. On the other hand, the hedged
index gained 11.0 percent in 1998 compared with 20.0 percent for an
unhedged index. Note, however, that the hedged index does not
include the cost of hedging.
Since it is difficult to predict which way the currency is going, is
it worthwhile spending money on currency hedging? There isn’t a
good answer. But as an investor, you should be aware of whether or
not the mutual fund you hold hedges currency risk.
International Investing and the Home Bias 255
The evidence presented in this chapter is based on past data. Since
future market conditions and market patterns may be completely
different, there is a small chance that home bias will not continue in
Of greater concern are the relative returns, risks, and correlations
of different markets. These may change in a way to make interna-
tional investing less attractive. However, the discussion in “Con-
cerns and Limitations” addresses these issues and continues to
recommend investing in foreign markets.
• Investors are risk-averse and would like to minimize risk or be
compensated for assuming any risk. Portfolio risk can be re-
duced by adding stocks that are not well correlated with the
portfolio. In particular, the risk can be reduced by adding for-
eign stocks to a domestic portfolio because foreign stocks are
not highly correlated with domestic stocks. Though holding
foreign stocks is optimal, investors tend not to hold portfolios
that contain an optimal exposure to foreign stocks. The
underweighting of foreign stocks in a portfolio is referred to as
the home bias.
• The evidence shows that the correlation between emerging
markets and the U.S. market is 0.42, and that between the de-
veloped markets and the U.S. market is 0.58. If emerging mar-
ket stocks and other developed market stocks are included in
a domestic portfolio, there is an improvement in the risk-re-
turn trade-off from a U.S. investor’s portfolio.An optimal port-
folio should contain about a 30 percent investment in other
developed markets and another 10 percent in emerging mar-
kets. Compared to the optimal portfolio, U.S. investors invest
only 7 percent in foreign stocks, emerging and developed mar-
kets combined. If other kinds of assets are considered, the home
bias becomes even more severe.
• It is possible that the benefits of international investing are over-
stated, as the analysis does not account for varying correlations,
trading costs and taxes, and different types of risk. These con-
cerns are addressed along with the likely reasons for persistence.
Beyond the Random Walk256
• Avenues for investing internationally includeAmerican deposi-
tory receipts, exchange-traded funds, and international mu-
tual funds. With the availability of these instruments, an
investor can realize the benefits of international investing with-
out directly owning foreign stocks.
• Whether or not to hedge foreign portfolios against currency
risk is a difficult question. While reducing risk is good, the cost
of hedging currency risk may turn out to be too high. Some
actively managed mutual funds do hedge currency risk, while
others do not.
Internationalizing a domestic portfolio is strongly recommended.
Research based on the 1976–99 period estimates that an investment
in developed countries and emerging markets would have increased
a U.S. investor’s annual return by 3.78 percent while reducing the
investor’s risk by 9.74 percent. Ideally, about 40 percent of the port-
folio should be invested in foreign securities through ADRs, ex-
change-traded funds, and international mutual funds.
http://www.msci.com: Morgan Stanley Capital International (MSCI) indexes
are most widely used for measuring performance of international markets.
The definition of the indexes and some performance data are available at
http://www.globalfindata.com: Global Financial Data is a warehouse for a
variety of financial data, including international stock returns and exchange
http://www.barra.com: Barra provides a downloadable file that contains
monthly S&P 500 total returns from 1975. These data are not available at the
Standard and Poor’s site (www.spglobal.com).
http://www.elkinsmcsherry.com: Estimates of trading costs mentioned in the
chapter are obtained from Elkins/McSherry. However, their website does
not provide this information.
http://www.ftmarketwatch.com and http://www.europeaninvestor.com:
Information on European stocks.
http://www.beri.com and http://www.eiu.com: These sites provide informa-
tion on political and business risk in different countries.
Benefits of International Investing
http://www.sec.gov/answers/adrs.htm, http://www.fidelity.com, http://
www.troweprice.com: These sites of the SEC, Fidelity, and Vanguard have
International Investing and the Home Bias 257
downloadable brochures on why international investing is good. Many
other mutual fund companies and regulatory bodies provide similar
Avenues for International Investment
http://www.adr.com: J. P. Morgan’s site. It explains how ADRs are created and
the mechanics of trading. Contains a complete list of all ADRs.
http://www.adrbny.com: ADR site of Bank of New York. Contains a complete
list of all ADRs.
http://www.citibank.com/adr/www: ADR site of Citigroup. Contains a
complete list of all ADRs.
http://www.troweprice.com: Mutual fund sites of Vanguard, Fidelity and T.
http://www.ishares.com: This site covers the exchange-traded funds managed
by Barclays Global Investors.
http://www.amex.com: Select “ETFs,” then “Product Information,” then
choose “International” from the drop-down list to get a list of exchange-
References for Further Reading
Solnik, Bruno. 2000. International Investments, 4th edition (Reading, Mass.:Addison-
Wesley Longman Inc.).
Eun, Cheol, and Bruce Resnick. 2001. International Financial Management, 2nd edi-
tion (New York: McGraw-Hill).
Benefits of International Investing
Clarke, Roger G., and R. Matthew Tullis. 1999. How Much International Expo-
sure Is Advantageous in a Domestic Portfolio? Journal of Portfolio Management
French, Kenneth R., and James M. Poterba. 1991. Investor Diversification and In-
ternational Equity Markets. American Economic Review 81(2), 222–26.
Hunter, John E., and T. Daniel Coggin. 1990. An Analysis of the Diversification
Benefit from International Equity Investment. Journal of Portfolio Management
Kim, E. Han, and Vijay Singal. 1997. Are Open Markets Good for Foreign Inves-
tors and Emerging Nations? Journal of Applied Corporate Finance 10(3), 18–33.
Michaud, Richard O., Gary L. Bergstrom, Ronald D. Frashure, and Bran K.
Wolahan. 1996. Twenty Years of International Equity Investing. Journal of Port-
folio Management 23(1), 9–22.
Sarkar, Asani, and Kai Li. 2002. Should U.S. Investors Hold Foreign Stocks? Fed-
eral Reserve Bank of New York’s Current Issues in Economics and Finance 8(3), 1–6.
Wignall, Christian. 1994. Does International Investing Still Make Sense? Yes, and
Here’s Why. Journal of Investing 3(4), 12–17.
Beyond the Random Walk258
Explanations of the Home Bias
Coen, Alain. 2001. Home Bias and International Capital Asset Pricing Model with
Human Capital. Journal of Multinational Financial Management 11(4–5), 497–513.
Coval, Joshua D., and Tobias J. Moskowitz. 1999. Home Bias at Home: Local Eq-
uity Preference in Domestic Portfolios. Journal of Finance 54(6), 2045–73.
Goetzmann, William N., and Alok Kumar. 2001. Equity Portfolio Diversification.
NBER working paper no. 8686.
Hasan, Iftekhar, and Yusif Simaan. 2000. A Rational Explanation for Home Coun-
try Bias. Journal of International Money and Finance 19(3), 331–61.
Huberman, Gur. 2001. Familiarity Breeds Investment. Review of Financial Studies
Jeske, Karsten. 2001. Equity Home Bias: Can Information Cost Explain the Puzzle?
FRB Atlanta—Economic Review 86(3), 31–42.
Lewis, Karen K. 1999. Trying to Explain Home Bias in Equities and Consumption.
Journal of Economic Literature 37(2), 571–608.
Avenues for International Investment
Aiello, Scott, and Natalie Chieffe. 1999. International Index Funds and the Invest-
ment Portfolio. Financial Services Review 8(1), 27–35.
Dada, Joe, and T. Jon Williams. 1993. Is There a Shortcut to International Invest-
ing? Journal of Investing 2(4), 45–47.
Droms, William G., and David A. Walker. 1994. Investment Performance of Inter-
national Mutual Funds. Journal of Financial Research 17(1), 1–14.
Errunza, Vihang, Ked Hogan, and Mao-Wei Hung. 1999. Can the Gains from In-
ternational Diversification Be Achieved Without Trading Abroad? Journal of
Finance 54(6), 2075–107.
Eun, Cheol S., Richard Kolodny, and Bruce G. Resnick. 1994. The Role of Interna-
tional Mutual Funds for U.S. Investors. Advances in Investment Analysis and
Portfolio Management 2, 1–35.
1. Besides the author’s own analysis, this chapter is based on Clarke and Tullis
(1999), Coval and Moskowitz (1999), Huberman (2001), Errunza, Hogan, and
Hung (1999), Sarkar and Li (2002), Eun and Resnick (2001), and Solnik (2000).
Currency forward rates are determined in accordance with interest rate
parity, such that the total returns from investment in two risk-free assets
are identical. Equivalence of returns implies that the forward rate fore-
sees the currency with a higher interest rate falling in value. However,
the evidence reveals that currencies with higher interest rates do not
actually fall as much as implied by the forward rate, creating the for-
ward rate bias. A trading strategy that short-sells currencies with low
interest rates and buys currencies with high interest rates can generate
The topic of this chapter is different from other chapters: it is slightly
more complex and related to currencies rather than stocks, but it is
nonetheless extremely important.1
From a trading perspective, the
bias discussed in this chapter has been documented in several hun-
dred research papers and many books. Institutional investors, hedge
funds, banks, currency traders, and many other market profession-
als periodically try to take advantage of this bias. The forward rate
bias, as it is generally known, is also related to international invest-
ing and currency hedging.
Before discussing the bias in forward rates, some knowledge of
forward rates is desirable and is covered first. A spot exchange rate
is the rate at which two currencies are exchanged in the spot mar-
ket, which means that delivery will take place in two business days.
If the delivery is scheduled to take place more than two business
Bias in Currency Forward Rates
Beyond the Random Walk260
days later, then the forward rate applies. Thus, the forward rate is
the rate at which two currencies are exchanged more than two busi-
ness days later. The forward rate is set at the time the contract is
entered into, not at the time of delivery. The obvious question arises:
how is the forward rate determined? The forward rate is based on
interest rate parity, which is described below.
Consider two investments that are completely risk-free. Let the
first investment be one-year U.S. Treasury bills (investment A) and
the second investment be another one-year claim fully guaranteed
by the U.S. government (investment B). Assume further that there
are no transaction costs and no restrictions on short selling, and
both investments are equally difficult or easy to make. Under these
circumstances, both investment A and investment B must provide
the same return. If not, arbitrage profits can be earned. For example,
assume that investment Agenerates a return of 2.0 percent, whereas
investment B generates a return of 0.25 percent.As both investments
are risk-free, an investor will short-sell B and use the proceeds to
buy A. The investor will incur a cost of 0.25 percent in borrowing or
short-selling B but earn a return of 2.0 percent from A. Thus, the net
profit is 1.75 percent. This profit is risk-free and requires zero in-
vestment. Many investors will repeat this process. The higher de-
mand for A means that its price will rise, reducing its return from 2
percent. At the same time, the excessive selling of B will lower B’s
price, raising its return from 0.25 percent. The process will continue
until the returns from both investments become equal.
The basic idea is that two riskless securities or investments must
earn the same return, or else arbitrage profits can be made. Consider
introducing another currency by letting B be an investment in Japa-
nese one-year Treasury bills. Investment A continues as an invest-
ment in U.S. T-bills. As the claim on Japanese T-bills is guaranteed by
the Japanese government, investment B is still risk-free. Since both
investments are risk-free, they must generate the same return. Con-
sider an investor with $1 million who wants to invest for one year
and get the money back in U.S. dollars. To invest in A, he just buys T-
bills worth $1 million. After one year he will get $1.02 million. To
invest in B, he must go through the following four steps:
1. Convert U.S. dollars into yen at the spot exchange rate. If the
spot rate is $S0
per J¥, then the amount in J¥= 1 million ×(1/ S0
2. Invest the yen in Japanese T-bills at 0.25 percent.
3. Hold for one year and redeem the T-bills for yen after one year.
The investor receives J¥1 million ×(1/ S0
) ×(1+ 0.0025), in-
Bias in Currency Forward Rates 261
cluding interest. In a mathematical format, it is equal to [(1/S0
× (1 + iFC
4. Convert the yen into dollars at the exchange rate. If the rate is
per J¥, then the investor will receive $1 million × (1/S0
(1+ 0.0025) × F0
. In a mathematical format, it is equal to [(1/S0
× (1 + iFC
)] × F0
The amount after the four steps, that is, the investment in B, must
also equal $1.02 million if it is risk-free. The first two steps are risk-
free since they are executed right away and the third step is guaran-
teed by the Japanese government. Step 4 is potentially risky.
Therefore, a forward contract signed at inception is required to make
step 4 risk-free. With a forward contract, the investor is guaranteed
exchange at the forward rate, which will take place a year later. Let
the forward rate be F0
. With all four steps being risk-free, the amount
that the investor receives at the end of one year with investment B
should equal $1.02 million, the amount that he will get with invest-
ment A. Thus, $1 million × (1/S0
) × (1 + 0.0025) × F0
= $1.02 million.
In a mathematical format, it can be written as [(1/S0
) × (1 + iFC
)] × F0
= 1 + i$
The only unknown variable is F0
. Upon calculation, it turns out
= 1.0175 × S0
. More formally, the forward rate can be written
in the form given below, called interest rate parity (IRP):
where the i’s are the interest rates, F0
are the exchange rates
expressed as dollars per unit of foreign currency, and the periods
for the forward rate and interest rates are the same. That is, a six-
month forward rate requires the interest rates also to be for six-month
Reexamining the equation reveals that if i$
is greater than iFC
in the example here (2 percent for the U.S. and 0.25 percent for Ja-
pan), then F0
. The calculations showed that F0
= 1.0175 × S0
such a case, one J¥ should buy more dollars a year later. This indi-
cates that the forward rate reflects an appreciation of J¥ over the
next one year and a depreciation of the dollar.
Look at it another way. As the return from both investments must
be the same, the currency with the lower interest rate must reflect an
appreciation relative to the other currency so that its total return can
equal the interest earned by the higher-interest-rate currency. That
Beyond the Random Walk262
can only happen if the forward rate reflects an appreciation of the
currency with the lower interest rate. That way the forward rate en-
sures no difference in total returns and no opportunity for arbitrage.
The condition that the forward rate be set in accordance with in-
terest rate parity is pretty unforgiving. In the example considered,
the forward rate must reflect an appreciation of 1.75 percent for the
yen. If it doesn’t, then arbitrage profits can be earned and will con-
tinue to be earned until the forward rate does reflect an apprecia-
tion of 1.75 percent for the yen. In practice, violations of interest
rate parity do not remain for more than a few seconds because
arbitrageurs pounce to make a quick buck.
So far, so good. The problem is that the actual future spot rate,
the exchange rate one year later, may not necessarily reflect an ap-
preciation of the yen as predicted by the forward rate. The evidence
indicates that currencies with high interest rates do not fall sufficiently
to make the returns equal. That is, the returns on higher-interest-
rate currencies tend to be higher than the returns on low-interest-
In brief, the forward rate (F0
) is the rate at which currency exchanges
take place later but the rate is decided at the time of signing the
forward contract. The forward rate is determined based on interest
rate parity, which ensures the same return for two risk-free assets.
Any deviations from this condition are quickly arbitraged away.
Second, under normal conditions, the future spot exchange rate (S1
is expected to equal, on average, the forward rate. However, that
does not seem to occur.
Table 11.1 will clarify some of these points. All rates are expressed
in U.S. dollars per yen.
J¥, showing an appreciation of the yen relative to the spot exchange
Table 11.1 Spot Rates and Forward Rates
Time = 0 Spot (S0
) Forward (F0
) Time = 1 Spot (S1
January 16 0.009445 0.009592 March 15 0.009446
March 15 0.009446 0.009567 June 17 0.009187
June 17 0.009187 0.009290 Sept. 16 0.009078
Sept. 16 0.009078 0.009191 Dec. 15 0.008754
Bias in Currency Forward Rates 263
rate of $0.009445/J¥ on January 16 and reflecting the higher U.S.
interest rate. However, the actual future spot rate on March 15 is
$0.009446/J¥, which did not reflect the anticipated appreciation of
the yen. This trend continues for the remaining dates. On March 15,
the forward rate for delivery on June 17 is $0.009567/J¥ but it turns
out that the yen actually depreciates to $0.009187/J¥ instead of ap-
preciating by June 17. The Japanese yen continues to depreciate in
September and December, though the forward rate reflects an appre-
ciation based on the lower interest on Japanese treasury securities.
The above table is only a snapshot and is not a scientifically se-
lected period. The formal testing of forward rates vis-à-vis the ac-
tual future rates is set up below, beginning with interest rate parity.
The interest rate parity equation can be rewritten so that the differ-
ence in exchange rates is equal to the difference in interest rates:
0 0 0 0l l FC
n F n S i i− = −
Since the future spot rate (S1
) should equal the forward rate, the
above equation can be rewritten as:
1 0 0 0l l FC
n S n S i i− = −
This equation can be further generalized to the following form:
1 0 0 0l l FC
n S n S a b i i− = + −
where a is expected to be 0 and b is expected to be +1 if the forward rate
is unbiased, that is, on average equal to the actual future spot rate.
The empirical tests of the forward rate bias basically check
whether b turns out be 1 or not. If b is not equal to 1, then the for-
ward rate (F0
) is biased, as it is not equal, on average, to the future
spot rate (S1
). The empirical evidence relating to the value of b var-
ies with the time periods, currency pairs, observation periods, and
the methods used. However, the value of b is generally negative,
never equal to or greater than 1, and, on average, equal to –0.88
(negative, not positive or zero). This and similar evidence is the ba-
sis for the forward rate bias.
A few results are presented in Table 11.2 for three different peri-
ods. Note that much of the evidence here relies on the value of the
dollar relative to other major currencies, such as the German mark
Beyond the Random Walk264
(until 1998), Japanese yen, British pound, Canadian dollar, and the
Swiss franc. It can be seen that all values are negative, in fact, less
than –1 in a majority of the cases, rather than being equal to +1.
The first two columns above report results based on a one-month
forward rate, whereas the last one has the results based on a three-
month forward rate. The values of b become smaller for the 3-month
period, but they continue to be negative. So there is consistency in
the results, though the magnitude of b varies.
There are two particular instances where the estimates of b change
considerably. First, it seems that the value of b has increased in the
1990s, that is, become less negative, as shown in Table 11.3.
The second instance of a change is with the period for which the
forward rate is estimated. The longer the period, the higher and
more positive are the estimates of b, as in Table 11.4.
With a one-month forward rate, the estimates of b are negative in
Table 11.4 (except for the German mark). However, when the pe-
riod increases to one year, more of them become positive, and fi-
nally with the ten-year forward rate all of them become positive.
The second column below incorporates a time series adjustment,
making the results less comparable to the other results. What seems
obvious, though, is that it takes a lot to make b close to 1. And re-
member that just as with other areas of empirical research, research-
ers have to try very hard to get a result that is different from what
has been documented before. In this case, researchers have to use a
Table 11.2 Forward Rate Bias
b for 1980–87 b for 1974–90 b for 1980–98
Currency (1-month period) (1-month period) (3-month period)
Canadian dollar –1.94 –1.46 –0.52
German mark –4.51 –3.54 –0.65
Japanese yen –2.94 –1.81 –3.44
Swiss franc –5.22
British pound –4.72 –2.31 –2.04
Table 11.3 Change in Forward Rate Bias During the 1990s
b for 1980–88 b for 1989–98
British pound –5.10 +1.06
Canadian dollar –0.45 –0.69
German mark –3.15 –0.54
Japanese yen –4.52 –3.86
Bias in Currency Forward Rates 265
variety of elaborate techniques to make the value of b close to 1,
since numerous papers have already found that b is negative.
The reduction in bias for longer-term forward rates may result
because the long periods probably smooth out all fluctuations. How-
ever, the long holding periods are uninteresting and unrealistic for
currencies because most investors hold currencies, as an investment,
for relatively short periods of time.
The evidence shows that the average value of b is –1 instead of
+1. What does it mean? It implies that if U.S. interest rates are higher
than foreign rates by 1 percent, then the U.S. dollar appreciates by 1
percent instead of depreciating by 1 percent, as implied by the for-
ward rate. Thus, the forward rate seems to be severely biased. A
trading strategy arising out of this evidence is to hold the currency
with the higher interest rate. If that currency’s interest rate is higher
by 1 percent, you can expect to earn 2 percent more than if you held
the currency with the lower interest rate.
While the return is higher, the risk associated with that return
has not been explicitly considered. If an optimal currency portfolio,
consisting of the German mark, Japanese yen, Swiss franc, and the
British pound with the U.S. dollar as the risk-free asset, is formed,
then it has been found that the portfolio would have generated an
average excess return of 2.79 percent per year over the period No-
vember 1989 through June 1999. The Sharpe ratio for this portfolio
is 0.69 compared with a Sharpe ratio of 0.53 for the U.S. Treasury
index, 0.49 for an unhedged global Treasury index, 0.80 for a hedged
global Treasury index, and 0.95 for the S&P 500. The Sharpe ratio
for the S&P 500 is unusually high because of the high returns earned
by stocks during this period.
Overall, the evidence suggests that holding currencies can be a
superior form of investment than several other forms of investment,
after accounting for risk, even during the 1990s. Strategies based on
the forward rate bias are implemented and tested later with more
Table 11.4 Forward Rate Bias for Different Holding Periods
b (1 month) b (1 year) b (10 years)
for 1985–2000 1985–2000 1983–98
British pound –1.94 1.00 0.57
Canadian dollar –0.98 –0.46 1.10
German mark 1.21 1.67 0.83
Japanese yen –1.38 –0.18 0.49
Swiss franc –0.23 0.73
Beyond the Random Walk266
The previous section established that the forward rate is biased in
the sense that, on average, the actual future spot rate is not equal to
the forward rate. Moreover, the bias is predictable. The actual fu-
ture spot rate reflects an appreciation of the high-interest-rate cur-
rency, whereas the forward rate suggests a depreciation of the
currency with the higher interest rate.
The analysis above made certain implicit assumptions to claim
that the forward rate should be an unbiased predictor of the future
spot rate. It is time to make those assumptions explicit. Fuller de-
tails of these assumptions are in the explanations that follow.
• Investors are risk-neutral.
• Investors are rational.
• Markets are efficient, that is, prices reflect all available infor-
INVESTORS ARE RISK-AVERSE
One assumption for the unbiasedness of forward rates is that inves-
tors are risk-neutral, that is, they do not care about risk but care
only about total return. Such investors will always choose invest-
ments that have the highest expected return, irrespective of the as-
sociated risk. So they will be fully invested in biotech and
information technology stocks but will never buy insurance.
In reality, investors are not risk-neutral, they are risk-averse. Be-
ing risk-averse means that investors care about risk, and their choices
are based both on return and risk. Such investors may frequently
turn down high-return investments if they contain high risk, and
will always demand compensation for any risk that they assume.
These investors will also buy insurance, which has a negative re-
turn, if that insurance will lower the risk of large losses.
The problem is that with risk-averse investors, the forward rate
cannot be unbiased. Let us consider a risk-averse investor X who is
holding dollars but needs yen after a year. X has two alternatives:
either to hedge or to remain unhedged. To hedge, X would enter
into a forward contract to buy yen for dollars at the forward rate, F0
The hedged alternative removes all risk related to the exchange of
currencies. With the unhedged alternative, he will just wait for a
year to roll around and then exchange dollars for yen at the future
spot rate, S1
. Since the unhedged position is riskier, X will choose to
remain unhedged only if he has to pay fewer dollars per yen using
Bias in Currency Forward Rates 267
the future spot rate than what he would have to pay if he had used
the forward rate. Thus, to make X happy with an unhedged position,
must be less than F0
, since the exchange rates are measured as dol-
lars per yen (S1
Reverse the previous example, and consider an investor who is
holding yen and wants to convert to dollars after one year. The same
two choices confront Y. Remaining unhedged means that he will
dollars for each yen. Or he could hedge by using a forward
contract that ensures that he will receive F0
dollars for each yen.
Again, Y will choose to remain unhedged only if he gets more dol-
lars per yen than with a forward contract. So he wants S1
to be larger
It is needless to say that both S1
can’t be true. The
result implies that if investors are risk-averse, then the forward rate
cannot be equal to the future spot rate. In other words, the forward rate
cannot be unbiased.
In addition, since risk-averse investors demand compensation for
risk, riskier currencies must have higher returns. Which currency is
riskier? Higher interest rates usually go with higher inflation, and
higher inflation entails higher risk. Therefore, higher-interest-rate
currencies must provide a higher return than lower-interest-rate
currencies as a compensation for risk. This implication is consistent
with the observed changes in currency values: higher-interest-rate
currencies do not fall as much as suggested by the forward rate
because the holder must be compensated for risk. The next ques-
tion is whether the compensation for risk is too large or too small.
Ab of –1 means that a 1 percent difference in interest rates must be
compensated by a 2 percent difference in returns. That level of com-
pensation for risk is too high. The theoretical risk premium even for
the most risk-averse investors is less than one-fifth of the observed
risk premium. Thus, the risk of the higher-interest-rate currency can
only explain a small fraction of currency movements.
SMALL SAMPLE, OR THE PESO PROBLEM
The second explanation relates to a small-sample problem. The small
sample is relevant in currency markets because exchange rates were
generally fixed until 1971. Early studies in the 1980s that investi-
gated the forward rate bias had only about ten years of data. The
role of a small sample can be approached from two angles.
First, investors need time to learn. Initial errors in expectations
might have occurred because investors and other market partici-
pants did not fully understand currency markets. Based on their
Beyond the Random Walk268
prior beliefs, investors formed fully rational forecasts about the fu-
ture spot rate. However, as they discovered errors in those beliefs,
they revised and refined their expectations to be more realistic.
Moreover, forward markets were not fully developed in the 1970s,
so conclusions based on that sample are not necessarily representa-
tive of well-functioning currency markets.
The second part of the small-sample explanation assumes that
investors do not err in setting expectations about the future. In their
expectations, they incorporate the probability, albeit low, of certain
events that may or may not actually take place. Given a sufficiently
long time period, those expectations will be realized, the low-prob-
ability event will occur, and the value of b will come out close to 1.
One example frequently cited is that of the Mexican peso. If you
consider the sample period between 1955 and 1975, when the Mexi-
can peso was fixed relative to the dollar at $0.25 per peso, you will
find that there is a severe bias in forward rates. The peso, with its
relatively high interest rate, did not fall relative to the dollar. Thus,
anyone looking at the 1955–75 period would conclude that forward
rates are biased. However, a large devaluation of the peso occurred
in 1976. If the same analysis is redone with 1955–76 as the sample
period instead of 1955–75, there is no forward rate bias. Thus, the
investors and the markets